Parametric equations are commonly used to describe surfaces. Looking at parametric equations does not provide tangible information about an object. Thus through the use of physical materials, an understanding of the limitations of the materials allows someone to gain a broader understanding of the surface. A M$\ddot{o}$bius strip and Figure 8 Klein bottle were created through knitting due to the precision and steady increase in curvature allowed through knitting. A more standard Klein bottle was created through crochet due to the ease in creating quick increases in curvature. Both methods demonstrate the change in curvature for both surfaces where the M$\ddot{o}$bius strip and Figure 8 Klein bottle have slower changes in curvature, but the classic Klein bottle has a quicker change in curvature.

This project considers the potential impact of learning relations between hobby craft makers and formally educated makers. It questions how the craft based relationship of a formally educated artist and a self taught/amatuer maker can be renegotiated and implemented in a broader learning context. The artistic research aims to propose that a facet of ‘new knowledge’ in the field and future of contemporary art and craft production is one of togetherness; by embracing discomfort and the unfamiliar to affirm and reveal the knowns and unknowns of one's own practice and field. The question is considered in discussion with social/relational art practices, amatuer craft theory and gift theory. The project culminates both in this paper and an exhibition piece as part of Konstfack University College of Arts, Crafts and Design Spring Exhibition 2016.

Cette thèse porte sur la structure de Lie de la cohomologie de Hochschild, donnée par le crochet de Gerstenhaber. Plus précisément, on étudie la structure d'algèbre de Lie du premier groupe de cohomologie et la structure de module de Lie des groupes de cohomologie de Hochschild de certaines algèbres monomiales. Une algèbre monomiale est définie comme le quotient de l'algèbre de chemins d'un carquois par un idéal bilatère admissible engendré par un ensemble de chemins de longueur au moins deux. On utilise les données combinatoires intrinsèques à de telles algèbres pour étudier la structure de Lie définie sur la cohomologie de Hochschild. En fait, on examine deux aspects de cette structure algébrique. Le premier est la relation entre la semi-simplicité du premier groupe de cohomologie de Hochschild et la nullité des groupes de cohomologie de Hochschild. Dans le second aspect, on se concentre sur la structure de module de Lie des groupes de cohomologie de Hochschild d'une famille d'algèbres particulière: celles dont le radical de Jacobson au carré est nul.

<p>Detta arbete har två syften. Det ena syftet är att beskriva virkningens utveckling i Sverige från de först kända föremålen fram till 1900-talets början. Det andra syftet är att initiera forskning inom den textila tekniken virkning. Med utgångspunkt i dessa syften har jag arbetat utifrån följande problemformuleringar. När har tekniken virkning börjat användas och hur kan den ha uppstått? Hur har virkningen utvecklats? Vilka termer har använts för att beskriva tekniken? Hur har virkningen varit ansedd under den undersökta perioden? Min ansats har varit hermeneutisk och arbetet är utfört i form av en kvalitativ och deskriptiv litteraturstudie. Det innebär att jag har tolkat texter kring tekniken virkning för att sedan begränsa och strukturera urvalet.</p><p>Arbetet visar på att virkning är en, i förhållande till andra textila tekniker, ung teknik. Tidigare har tekniken tidigast kunna dateras till slutet av 1700-talet. En virkad pung hos Kungliga Myntkabinettet med dateringen 1693 gör att jag vill korrigera dateringen till 1600-talet. Det är osäkert hur tekniken virkning har uppstått, två teorier är att tekniken ska ha sitt ursprung i påtning eller tambursömmen. Arbetets ståndpunkt är dock att en kombination av påtning och tambursöm är ett troligare ursprung. Det är i samband med industrialiseringen av Europa som virkningen växer fram som teknik. Det kan förklaras med en ökad garntillgång och billigare virkbeskrivningar. Vidare belyser arbetet den flora av termer som de första virkbeskrivningarna innehåller. Avslutningsvis behandlas virkningens anseende med utgångspunkt i den debatt som pågick vid slutet av 1800-talet.</p>

Detta arbete har två syften. Det ena syftet är att beskriva virkningens utveckling i Sverige från de först kända föremålen fram till 1900-talets början. Det andra syftet är att initiera forskning inom den textila tekniken virkning. Med utgångspunkt i dessa syften har jag arbetat utifrån följande problemformuleringar. När har tekniken virkning börjat användas och hur kan den ha uppstått? Hur har virkningen utvecklats? Vilka termer har använts för att beskriva tekniken? Hur har virkningen varit ansedd under den undersökta perioden? Min ansats har varit hermeneutisk och arbetet är utfört i form av en kvalitativ och deskriptiv litteraturstudie. Det innebär att jag har tolkat texter kring tekniken virkning för att sedan begränsa och strukturera urvalet. Arbetet visar på att virkning är en, i förhållande till andra textila tekniker, ung teknik. Tidigare har tekniken tidigast kunna dateras till slutet av 1700-talet. En virkad pung hos Kungliga Myntkabinettet med dateringen 1693 gör att jag vill korrigera dateringen till 1600-talet. Det är osäkert hur tekniken virkning har uppstått, två teorier är att tekniken ska ha sitt ursprung i påtning eller tambursömmen. Arbetets ståndpunkt är dock att en kombination av påtning och tambursöm är ett troligare ursprung. Det är i samband med industrialiseringen av Europa som virkningen växer fram som teknik. Det kan förklaras med en ökad garntillgång och billigare virkbeskrivningar. Vidare belyser arbetet den flora av termer som de första virkbeskrivningarna innehåller. Avslutningsvis behandlas virkningens anseende med utgångspunkt i den debatt som pågick vid slutet av 1800-talet.

In this project a collection of clothing, based on the handicraft of knitting and crocheting, has been developed. Today most garments are produced on industrial machines, cheaply, fast and with a low quality. An alternative to this is slow fashion which aims for long-lasting, locally manufactured clothing, primarily made from sustainably sourced fair-trade fabrics. The aim of this project is to raise awareness of slow fashion by working with the handicraft of knitting and crochet. The work has a slow process of making, and the items are carefully made by hand which raises the value of the garments and is a more sustainable way of using the materials.  Traditional flat pattern construction is based on symmetrical squares and vertical and horizontal lines. This work's construction is based on diagonal lines around the women's body, as a suggestion that it fits the knitted fabric property and the women's body better. Design decisions were made by looking at renaissance fashion and paintings. To highlight an older way of making fashion and to push the expression in knitwear and show the potential in the craft.

Textile waste, both pre and post consumer, is a problem that needs a solution, and fast. This work aims to find a simple solution to that problem, to exemplify how a small change in thinking and structures can make a big difference. The proposal is a design system of square construction, with roots in historical fabric conservancy practices and by use of salvage craft techniques. By constructing garments out of squares, waste is eliminated by simple means and existing materials of different qualities can be cut in the same way, thereby rationalized, then assembled into larger materials and so an up cycling process is achieved. The result of this work is a versatile design system which may lead to many different outcomes in the hands of different designers without compromising on desired fit and without the waste generated from cutting conventionally. In the present fashion field solutions such as this system are necessary to encourage the apprehensive designer to take steps towards sustainable practices.

In the Surface Development Test, self-perceived Sewing Expertise was significant in predicting participants' test scores. For the Paper Folding Test, Knitting and Crocheting Expertise were significant, suggesting expertise may mitigate age effects.; Spatial ability has been a topic of much research and debate over the past few decades. Yet, there are gaps in the current literature. Spatial ability refers to the aptitude of an individual to mentally rotate objects, visualize spaces, and recognize patterns (Linn & Petersen, 1985). A highly spatial task that is not addressed in research literature is crafting. Crafting may refer to knitting, crocheting, sewing, and other hobbies that include manipulations of materials. These crafts are spatially oriented, because they necessitate mental rotation, pattern recognition, and 3-D visualization to create an object. While research tends to favor males on certain spatial tests (Voyer, Voyer, & Bryden, 1995), research on the relationship between expertise and spatial ability has concentrated on traditionally male dominated domains, such as architecture and video games (Salthouse & Mitchell, 1990; Sims & Mayer, 2002). The traditionally female domain of needlework crafting expertise has not been studied empirically. First, a literature review is presented to give an overview of previous spatial ability research. The paper then describes the needlework crafts of sewing, knitting, and crocheting, including their historical significance and the spatial processes involved. A study was conducted to test the hypothesis that more expertise in needlework crafts will correlate with better performance on spatial ability tests. Three hundred and four adult women (ages 18-77) completed the study. Participant experience level was determined by self-perceived level of crafting expertise. Participants performed three spatial ability tests from the ETS Factor Reference Kit (Ekstrom et al., 1976): Paper Folding, Surface Development, and Card Rotations. Results indicated that age was correlated negatively with performance in all spatial tests. Only age was significant in the Card Rotations Test.

Aufgrund der Klimakrise und der Notwendigkeit CO2-Emissionen zu reduzieren, ist in Zukunft mit einer steigenden Nachfrage an Leichtbaumaterialien wie textilverstärkten Verbundwerkstoffen zu rechnen. Aufgrund steigender Rohstoff- und Energiekosten verspricht der Einsatz von endkonturnahen Verbundwerkstoffen eine Reduktion der Herstellungskosten und des Abfalls. Herkömmliche Textiltechnologien sind nur begrenzt in der Lage die erforderlichen komplex geformten Textilien herzustellen. Um dieses Problem durch den Einsatz alternativer, noch nicht industriell etablierter Technologien zu lösen, beschäftigt sich diese Arbeit ausführlich mit der Entwicklung einer Häkelmaschine sowie der Untersuchung entsprechender Textilien. Häkeln ist eine maschenbildende Technologie, bei der im Gegensatz zum Stricken die Schlaufen, die eine Masche bilden, sowohl vertikal als auch horizontal aus zuvor gebildeten Maschen entspringen. Mit dem vielseitigen Häkeln ist es insbesondere möglich, komplexe dreidimensionale (3D) Formen zu erzeugen, da an jeder beliebigen Stelle eines Textils neue Maschen gebildet werden können. Bisherige Häkelmaschinenansätze sind unzureichend und bezüglich ihrer Skalierbarkeit zu einer industriell einsetzbaren Maschine stark eingeschränkt. Industriell etablierte Maschinen, die Häkelmaschinen genannt werden, sind in ihrer Bezeichnung irreführend, da es sich um Wirkmaschinen handelt, die nur grob die Häkelstruktur nachahmen, aber keine echten Häkelmaschen bilden können. Die hier entwickelte und patentierte Häkelmaschine namens Crochet Automaton (CroMat) ermöglicht erstmals die automatisierte Herstellung von Luftmaschen, Kettmaschen, festen Maschen, halben Stäbchen, Übergängen der Maschenreihen, Zunahmen sowie Abnahmen und auch anderen Operationen nach dem Prinzip des Flachhäkelns auf Basis einer Luftmaschenreihe. Darüber hinaus können neue Maschen durch ein manuelles Umhängen des produzierten Textils an nahezu beliebigen Stellen gebildet werden. Damit können komplex geformte 3D-Textilien entsprechend den Vorteilen des Häkelns hergestellt werden. Mit dem entwickelten CroMat-Prototyp lassen sich Formen herstellen, die für endkonturnahe Faserverbundwerkstoffe wie bspw. Doppel-T-Träger potenziell geeignet sind. Durch ein Aufhängen verschiedener Maschenreihen oder Textilien auf denselben Nadeln der Maschine ist es ebenfalls möglich diese mit dem Häkeln einer verbindenden Reihe zu fügen. Neben dem mechatronischen Prototyp mit zehn Achsen wird das weltweit erste Software-Tool für den Entwurf von maschinell gehäkelten Textilien entwickelt. Es beinhaltet eine Fehlerüberprüfung, die automatische Generierung des G-Codes für die Maschinensteuerung und eine Vorschau der entworfenen Textilien. Neben einer grafischen Benutzeroberfläche mit standardisierten Häkelsymbolen wird auch die Möglichkeit zur automatischen Generierung der Häkelstruktur entsprechend der Form eines zweidimensionalen (2D) Polygons geboten. Für die Vorschau wurde das erste Topologie-basierte Modellierungs-Framework für maschinell herstellbare Häkelstrukturen entwickelt. Eine ähnliche Modellierung wurde für manuell gehäkelte Stoffe entwickelt, die sich von den maschinell hergestellten nur darin unterscheiden, dass der Stoff nach jeder Reihe gewendet wird und somit die Maschen von verschiedenen Seiten aus gebildet werden. Beide Modellarten können als Grundlage für simulative Untersuchungen mit der Finite-Elemente-Methode (FEM) verwendet werden, die in dieser Arbeit zum ersten Mal zur Simulation von gehäkelten Textilien eingesetzt wurde. Darüber hinaus wurden erstmals die Zugeigenschaften von manuell gehäkelten Textilien systematisch untersucht und die Eigenschaften der ersten Faserverbundwerkstoffe mit gehäkelten Textilien erforscht. Gehäkelte Textilien (und entsprechende Verbundstoffe) haben grundsätzlich ähnliche Eigenschaften wie gestrickte Textilien, können aber tendenziell höheren Kräften standhalten. Zusammen mit den Formgebungsmöglichkeiten ist die CroMat-Häkelmaschine generell vielversprechend für die Automatisierung des Häkelns und insbesondere für die zukünftige Produktion von endkonturnahen Faserverbundwerkstoffen.:1 Introduction 1 1.1 Motivation 1 1.2 Aim 2 1.3 Work structure 3 2 Technical and scientific background 4 2.1 Crochet 4 2.1.1 Technique and stitch formation 5 2.1.2 Crocheting a fabric 8 2.1.3 Applications of crochet 11 2.1.4 Research overview on crochet 11 2.2 Knitting machines 15 2.2.1 Weft knitting 16 2.2.2 Warp knitting 19 2.2.3 Crochet gallon machines 21 2.3 Existing crochet machine approaches 23 2.3.1 First approach to automate crochet 23 2.3.2 Circular crochet machine approach 25 2.3.3 Crocheting with a robotic arm 27 2.3.4 Further attempts to automate crocheting 29 2.4 Rapid prototyping 30 2.4.1 Development approach 30 2.4.2 3D printing 31 2.5 Electric motors 33 2.5.1 Stepper 33 2.5.2 Servo motors 34 2.5.3 G-code 35 2.6 Textile composites 37 2.6.1 Composite production 37 2.6.2 Near net-shaped composites 38 3 Crochet machine development 39 3.1 CroMat innovation process 39 3.1.1 Development phases 39 3.1.2 Analyzing the first crochet machine approach 41 3.1.3 Definition of crochet machine prototype requirements 43 3.1.4 Crochet needle insertion process 47 3.1.5 Suspending stitches on auxiliary needles 55 3.1.6 Yarn guide and patent 57 3.2 Improvements beyond the patent 60 3.2.1 Analyzing the yarn feeding problem 60 3.2.2 Systematic identification of possible solutions 61 3.2.3 Implementation of the most suited solution 64 3.3 Automated crochet stitch formation 67 3.3.1 Initial situation 67 3.3.2 Slip stitch 68 3.3.3 Single crochet 71 3.3.4 Half double crochet 73 3.3.5 Turn 75 3.3.6 Chain stitch and skipping a stitch within a course 77 3.3.7 Increase stitches 79 3.3.8 Decrease stitches 82 3.3.9 Further methods for changing the fabric’s width 84 3.3.10 More complex stitches 87 3.4 Technical implementation of CroMat prototype 89 3.4.1 CroMat machine overview 89 3.4.2 Auxiliary needles 94 3.4.3 Crochet needle 100 3.4.4 Yarn guide 106 3.4.5 Stress on yarn and machine elements 109 3.4.6 Yarn tension 115 3.4.7 Firmware and motor control 117 3.5 Crocheting with the CroMat prototype 120 3.5.1 Producing an exemplary crocheted fabric 120 3.5.2 Movements for SC formation 122 3.6 Development of CroMat crochet design tool 125 3.6.1 Tool overview 125 3.6.2 User interface 126 3.6.3 Error checking 129 3.6.4 Preview of the fabric 130 3.6.5 Generating G-code 130 3.6.6 Discussing the design tool 132 3.7 CroMat requirement fulfillment 134 4 Research on crocheted fabrics 137 4.1 Modeling and simulation of manually crocheted fabrics 137 4.1.1 Modeling approaches for textiles 137 4.1.2 Developed modeling of crochet structures 138 4.1.3 FEM investigations 143 4.2 Mechanical characteristics of manually crocheted fabrics 146 4.2.1 Study overview 146 4.2.2 Materials and Methods 146 4.2.3 Influence of the crocheter 148 4.2.4 Influence of the crochet structure 150 4.2.5 Crochet composite 152 4.2.6 Evaluation of the results 155 4.3 Modeling and simulation of machine-crocheted fabrics 157 4.3.1 Modeling machine-crocheted fabrics 157 4.3.2 Modeling of INC and DEC 159 4.3.3 Simulative comparison of hand- and machine-crocheted fabrics 161 4.4 Generating machine producible crochet patterns in shapes of 2D polygons 164 4.4.1 Background 164 4.4.2 Developed polygon subdivision algorithm 165 4.4.3 Improving the subdivision’s quality 168 4.4.4 Crochet subdivision results for exemplary polygons 170 4.4.5 Discussing the results 176 4.5 Exemplary machine-crocheted fabrics 178 4.5.1 Basic fabric structure 178 4.5.2 Advanced possible structures 181 4.5.3 Poisson’s ratio investigation 185 5 Conclusion 189 5.1 Summary 189 5.2 Outlook 191 6 References 193 6.1 References of the author 193 6.2 Further references 193 / In the future, due to the climate crisis and the need to reduce CO2 emissions, an increasing demand for lightweight materials such as textile reinforced composites can be expected. Because of rising raw material and energy costs, the application of more near net-shaped composites is promising for reducing manufacturing costs and waste. However, conventional textile technologies are limited in their ability to produce the necessary complex-shaped textiles. In order to address this problem by using alternative technologies that have not yet been industrially established, this thesis deals extensively with the development of a crochet machine and the investigation of respective textiles. Crochet is a stitch-forming technology in which, unlike knitting, the loops of a stitch originate both vertically and horizontally from previously formed stitches. With versatile crochet, it is especially possible to create complex three-dimensional (3D) shapes because new stitches can be formed at any point on a fabric. Previous crochet machine approaches are inadequate and severely limited in scalability to an industrially applicable machine. Industrially established machinery called crochet machines are misleading in their designation because they are knitting machines that can only roughly mimic crochet structure but cannot form true crocheted fabrics. The Crochet Automaton (CroMat) crochet machine developed and patented here enables for the first time the automated production of chain stitches (CHs), slip stitches (SLs), single crochet stitches (SCs), half double crochet stitches (HDCs), turns (T1 and T2), increase stitches (INCs) as well as decrease stitches (DECs) and other operations according to the principle of flat crocheting based on a chain line. In addition, by manually removing and re-hanging the produced fabric, new stitches can be formed at almost any point to produce complex-shaped 3D textiles according to the capabilities of crochet. For example, it is possible to produce shapes relevant for near net-shaped composites such as double T-beams with the developed CroMat prototype. With manually suspending different stitch rows or fabrics on the machine, it is also possible to join them by simultaneously crocheting a course through them. In addition to the mechatronic prototype with ten axes, the world's first tool for designing machine-crocheted textiles is developed. It includes error checking, generation of the G-code for machine control and a preview of the designed fabrics. Beyond a graphical user interface (GUI) with standardized crochet symbols, a higher-level programmability is added through specifying a shape by 2D polygons and automatically generating corresponding, machine-crochetable patterns. The first topology-based modeling framework for machine-producible crochet structures was developed for the preview. A similar modeling was developed for manually crocheted fabrics, which differ from the machine-produced ones only in the fact that the fabric is turned after each row and thus the stitches are formed from different sides. Both models can be used as a basis for simulative finite element method (FEM) investigations, which were used in this work to simulate crocheted fabrics for the first time. Furthermore, the tensile properties of manually crocheted fabrics were systematically investigated for the first time and the properties of the first crochet composites were researched. Crocheted textiles (and corresponding composites) have basically similar properties as knitted textiles but have a tendency to withstand higher forces. Together with the shaping capabilities, the CroMat crochet machine is generally highly promising for the automation of crochet and especially for the future production of near net-shaped composite reinforcements.:1 Introduction 1 1.1 Motivation 1 1.2 Aim 2 1.3 Work structure 3 2 Technical and scientific background 4 2.1 Crochet 4 2.1.1 Technique and stitch formation 5 2.1.2 Crocheting a fabric 8 2.1.3 Applications of crochet 11 2.1.4 Research overview on crochet 11 2.2 Knitting machines 15 2.2.1 Weft knitting 16 2.2.2 Warp knitting 19 2.2.3 Crochet gallon machines 21 2.3 Existing crochet machine approaches 23 2.3.1 First approach to automate crochet 23 2.3.2 Circular crochet machine approach 25 2.3.3 Crocheting with a robotic arm 27 2.3.4 Further attempts to automate crocheting 29 2.4 Rapid prototyping 30 2.4.1 Development approach 30 2.4.2 3D printing 31 2.5 Electric motors 33 2.5.1 Stepper 33 2.5.2 Servo motors 34 2.5.3 G-code 35 2.6 Textile composites 37 2.6.1 Composite production 37 2.6.2 Near net-shaped composites 38 3 Crochet machine development 39 3.1 CroMat innovation process 39 3.1.1 Development phases 39 3.1.2 Analyzing the first crochet machine approach 41 3.1.3 Definition of crochet machine prototype requirements 43 3.1.4 Crochet needle insertion process 47 3.1.5 Suspending stitches on auxiliary needles 55 3.1.6 Yarn guide and patent 57 3.2 Improvements beyond the patent 60 3.2.1 Analyzing the yarn feeding problem 60 3.2.2 Systematic identification of possible solutions 61 3.2.3 Implementation of the most suited solution 64 3.3 Automated crochet stitch formation 67 3.3.1 Initial situation 67 3.3.2 Slip stitch 68 3.3.3 Single crochet 71 3.3.4 Half double crochet 73 3.3.5 Turn 75 3.3.6 Chain stitch and skipping a stitch within a course 77 3.3.7 Increase stitches 79 3.3.8 Decrease stitches 82 3.3.9 Further methods for changing the fabric’s width 84 3.3.10 More complex stitches 87 3.4 Technical implementation of CroMat prototype 89 3.4.1 CroMat machine overview 89 3.4.2 Auxiliary needles 94 3.4.3 Crochet needle 100 3.4.4 Yarn guide 106 3.4.5 Stress on yarn and machine elements 109 3.4.6 Yarn tension 115 3.4.7 Firmware and motor control 117 3.5 Crocheting with the CroMat prototype 120 3.5.1 Producing an exemplary crocheted fabric 120 3.5.2 Movements for SC formation 122 3.6 Development of CroMat crochet design tool 125 3.6.1 Tool overview 125 3.6.2 User interface 126 3.6.3 Error checking 129 3.6.4 Preview of the fabric 130 3.6.5 Generating G-code 130 3.6.6 Discussing the design tool 132 3.7 CroMat requirement fulfillment 134 4 Research on crocheted fabrics 137 4.1 Modeling and simulation of manually crocheted fabrics 137 4.1.1 Modeling approaches for textiles 137 4.1.2 Developed modeling of crochet structures 138 4.1.3 FEM investigations 143 4.2 Mechanical characteristics of manually crocheted fabrics 146 4.2.1 Study overview 146 4.2.2 Materials and Methods 146 4.2.3 Influence of the crocheter 148 4.2.4 Influence of the crochet structure 150 4.2.5 Crochet composite 152 4.2.6 Evaluation of the results 155 4.3 Modeling and simulation of machine-crocheted fabrics 157 4.3.1 Modeling machine-crocheted fabrics 157 4.3.2 Modeling of INC and DEC 159 4.3.3 Simulative comparison of hand- and machine-crocheted fabrics 161 4.4 Generating machine producible crochet patterns in shapes of 2D polygons 164 4.4.1 Background 164 4.4.2 Developed polygon subdivision algorithm 165 4.4.3 Improving the subdivision’s quality 168 4.4.4 Crochet subdivision results for exemplary polygons 170 4.4.5 Discussing the results 176 4.5 Exemplary machine-crocheted fabrics 178 4.5.1 Basic fabric structure 178 4.5.2 Advanced possible structures 181 4.5.3 Poisson’s ratio investigation 185 5 Conclusion 189 5.1 Summary 189 5.2 Outlook 191 6 References 193 6.1 References of the author 193 6.2 Further references 193

Dans cette thèse, nous étudions divers problèmes issus de la topologie symplectique où la topologie C° intervient. Nous étudions diverses complétions de l'espace des applications hamiltoniennes, puis appliquons cette étude aux équations d'Hamilton-Jacobi. Nous abordons ensuite le problème de l'extension du morphisme de Calabi à des groupes d'homéomorphismes. Enfin, nous nous intéressons à la rigidité C° du crochet de Poisson et à l'extension au cadre C° de la notion de représentation hamiltonienne.