Dans cette thèse, on étudie les propriétés des sous-variétés lagrangiennes dans une variété symplectique en utilisant la relation de cobordisme lagrangien. Plus précisément, on s'intéresse à déterminer les conditions pour lesquelles les cobordismes lagrangiens élémentaires sont en fait triviaux. En utilisant des techniques de l'homologie de Floer et le théorème du s-cobordisme on démontre que, sous certaines hypothèses topologiques, un cobordisme lagrangien exact est une pseudo-isotopie lagrangienne. Ce resultat est une forme faible d'une conjecture due à Biran et Cornea qui stipule qu'un cobordisme lagrangien exact est hamiltonien isotope à une suspension lagrangianenne. / In this thesis we study the properties of Lagrangian submanifolds of a symplectic manifold by using the relation of Lagrangian cobordism. More precisely, we are interested in determining when an elementary Lagrangian cobordism is trivial. Using techniques coming from Floer homology and the s-cobordism theorem, we show that under some topological assumptions, an exact Lagrangian cobordism is a Lagrangian pseudo-isotopy. This is a weaker version of a conjecture proposed by Biran and Cornea, which states that any exact Lagrangian cobordism is Hamiltonian isotopic to a Lagrangian suspension.

Submitted by Izabel Franco (izabel-franco@ufscar.br) on 2016-09-23T19:38:10Z No. of bitstreams: 1 DissGCIF.pdf: 1709329 bytes, checksum: 237db6a30fde160e22a9171ebb48cdb8 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-26T20:45:16Z (GMT) No. of bitstreams: 1 DissGCIF.pdf: 1709329 bytes, checksum: 237db6a30fde160e22a9171ebb48cdb8 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-26T20:45:22Z (GMT) No. of bitstreams: 1 DissGCIF.pdf: 1709329 bytes, checksum: 237db6a30fde160e22a9171ebb48cdb8 (MD5) / Made available in DSpace on 2016-09-26T20:45:29Z (GMT). No. of bitstreams: 1 DissGCIF.pdf: 1709329 bytes, checksum: 237db6a30fde160e22a9171ebb48cdb8 (MD5) Previous issue date: 2015-04-22 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / The nonabelian tensor square GG of a group G was introduced by R. K. Dennis [8] in a search for new homology functors having a close relationship to K-theory and it is based on the work of C. Miller [14]. Subsequently R. Brown and J.-L. Loday [6] discovered a topological significance for the tensor square, namely, that the third homotopy group of the suspension of an Eilenberg MacLane space K(G; 1) satisfies _3 �����SK(G; 1) _ _= ker(_1), where _1 : GG ! G is the “comutator homomorphism”: _1(gh) = [g; h] = ghg�����1h�����1, 8g; h 2 G. They also defined the tensor product GH of two distinct groups acting “compatibly” on each other and showed that it arose in a certain “universal crossed square”. The main purpose of this work is to present the first properties of the nonabelian tensor product of groups and its applications in homotopy theory. / O quadrado tensorial não-abeliano GG de um grupo G foi introduzido por R. K. Dennis [8] em uma busca por novos funtores de homologia tendo uma íntima relação com a K-teoria e é baseado no trabalho de C. Miller [14]. Após isso, R. Brown e J.-L. Loday [6] descobriram uma importância topológica para o quadrado tensorial, a saber, que o terceiro grupo de homotopia da suspensão de um espaço de Eilenberg MacLane K(G; 1) satisfaz _3 SK(G; 1) __= ker(_1), em que _1 : G G ! G é o “homomorfismo comutador”: _1(gh) = [g; h] = ghg1h1, 8g; h 2 G. Os autores também definiram o produto tensorial GH de dois grupos quaisquer agindo “compativelmente” um no outro e mostraram que este aparece em um certo “quadrado cruzado universal”. O objetivo desse trabalho é apresentar o produto tensorial de grupos não-abelianos, suas primeiras propriedades e a aplicação dele na teoria de homotopia. / Processo 2013/01245-7

À toute variété de contact, on peut associer canoniquement une variété symplectique appelée sa symplectisation de sorte que la géométrie de contact peut se reformuler en termes de géométrie symplectique équivariante. Au sujet de cette construction fondamentale, une question basique restait ouverte : si deux variété de contact ont des symplectisations isomorphes sont-elles isomorphes ? On construit dans cette thèse des contre-exemples à cette question. Il existe en effet, en toute dimension impaire supérieure ou égale à 5, des variétés de contact non difféomorphes admettant pourtant des symplectisations isomorphes. On construit également, sur une même variété deux structures de contact non conjuguées par un difféomorphisme mais admettant des symplectisations isomorphes. Les démonstrations sont basées sur un phénomène bien connu en topologie différentielle (l'existence de h-cobordismes non triviaux, détectée par la torsion de Whitehead) ainsi que sur des résultats de flexibilité en géométrie symplectique dus à Cieliebak et Eliashberg. Un autre résultat de cette th?e affirme que ces variété de contact, bien que non isomorphes, le deviennent toutefois après un nombre suffisant de sommes connexes avec un produit de sphères. / To any contact manifold one can associate a symplectic manifold called its symplectisation in such a way that contact geometry can be reformulated in terms of equivariant symplectic geometry. Concerning this fundamental construction, a basic question remained open : if two contact manifolds have isomorphic symplectizations, are they isomorphic ? In this thesis, we construct counter-examples to this question. Indeed, in any odd dimension greater than or equal to 5, there exist non-diffeomorphic contact manifolds with isomorphic symplectisations. In addition, we construct two contact structures on a closed manifold that are not conjugate by a diffeomorphism though their symplectizations are isomorphic. The proofs are based on a well-known phenomenon in differential topology (the existence of non-trivial h-cobordisms, detected by Whitehead torsion) as well as flexibility results in symplectic geometry due to Cieliebak and Eliashberg. Another result from this thesis asserts that though these contact manifolds are not isomorphic, they become so after sufficiently many connect sum with a product of spheres.

This dissertation is an investigation into the classification of all hyperbolic manifolds which admit a reducible Dehn filling and a toroidal Dehn filling with distance 3. The first example was given by Boyer and Zhang. They used the Whitehead link. Eudave-Muñoz and Wu gave an infinite family of such hyperbolic manifolds using tangle arguments. I show in this dissertation that these are the only hyperbolic manifolds admitting a reducible Dehn filling and a toroidal Dehn filling with distance 3. The main tool to prove this is to use the intersection graphs on surfaces introduced and developed by Gordon and Luecke. / text

This dissertation presents a Whiteheadian interpretation of the notions of mind, immanence and process as they are addressed in the Zohar. According to many scholars, this kabbalistic creation story as portrayed in the Zohar is a reaction to the earlier rabbinic concept of God qua creator, which emphasized divine transcendence over divine immanence. The medieval Jewish philosophers, particularly Maimonides influenced by Aristotle, placed particular emphasis on divine transcendence, seeing a radical separation between Creator and creation. With this in mind, these scholars claim that one of the goals of the Zohar’s creation story was to emphasize God’s immanence within creation. Similar to the Zohar, the process metaphysics of Alfred North Whitehead and his followers was reacting to the substance metaphysics that had dominated Western philosophy as far back as ancient Greek thought. Whitehead adopts a very similar narrative to that of the Zohar. First there is mind containing all the eternal objects which serve as potential for the creation (God’s primordial nature). Mind becomes immanent in all actual occasions through prehension (God’s consequent nature). Finally God becomes “the lure” (to use Whitehead’s phrase) in the ongoing process of nature (God as superject). In this narrative, God is not the static being, the unmoved mover as discussed by Aristotle, but rather, is portrayed as a dynamic becoming, a God of process. Due to these significant similarities between Whitehead’s process philosophy and the Zohar with regard to the immanence of God and the process of creation, it is worthwhile to attempt a process interpretation of the kabbalistic creation story. The first part of this dissertation is entitled Philosophical Foundations, focusing on the intellectual framework of this study of the Zohar. The second part is entitled Creating a Narrative, looking at the text of the Zohar through the lens of Whitehead’s metaphysics. Finally, the conclusion looks at the narrative and discusses whether the goals of the dissertation have been achieved. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

Title from PDF of title page. / Document formatted into pages; contains 58 pages / Thesis (M.A.)--University of South Florida, 2003. / Includes bibliographical references. / Text (Electronic thesis) in PDF format. / ABSTRACT: In this thesis I examine three models of justification for the epistemic authority of the principle of contradiction. Aristotle has deemed the principle "that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect" the most certain and most prior of all principles, both in the order of nature and in the order of knowledge, and as such it is indemonstrable. The principle of contradiction is involved in any act of rational discourse, and to deny it would be to reduce ourselves to a vegetative state, being incapable of uttering anything with meaning. The way we reach the principle of contradiction is by intuitive grasping (epagoge) from the experience of the particulars, by recognizing the universals in the particulars encountered, and it is different from simple induction, which, in Mill's view, is the process through which we construct a general statement on the basis of a limited sample of observed particulars. / ABSTRACT: Hence, the principle of contradiction, being a mere generalization from experience, through induction, loses its certainty and necessity. Even though it has a high degree of confirmation from experience, it is in principle possible to come across a counter-example which would refute it. Mill's account opens the path to the modern view of the principle of contradiction. In Principia Mathematica, Russell and Whitehead contend that the principle of contradiction is still a tautology, always true, but it is derived from other propositions, set forth as axioms. Its formulation, " (p & p)" is quite different from Aristotle's, and this is why we are faced with the bizarre situation of being able to derive the law of contradiction in a formal system which could not have been built without the very principle of which the law is an expression of. / ABSTRACT: This is perhaps because the principle of contradiction, as a principle, has a much larger range of application and is consequently more fundamental than what we call today the law of contradiction, with its formal function. / System requirements: World Wide Web browser and PDF reader. / Mode of access: World Wide Web.

In his thesis we are concerned with certain numerical invariants of homotopy type akin to the Lusternik-Schnirelmann category and cocategory. In a series of papers I. Bernstein, T. Ganea, and P.J. Hilton developed the concepts of the category and weak category of a topological space. They also considered the related concepts of conilpotency and cup product length of a space and the weak category of a map. Later T. Ganea gave another definition of category and weak category (which we shall write as G-cat and G-wcat) in terms of vibrations and cofibrations and hence this dualizes easily in the sense of Eckmann-Hilton. We find the relationships between these invariants and then find various examples of spaces which show that the invariants are all different except cat and G-cat. The results are contained in the following theorem. The map $e:B -> OmegaSigma B$ is the natural embedding. All the invariants are normalized so as to take the value 0 on contractible spaces. THEOREM Let B have the homotopy type of a simply connected CW-complex, then $cat B = G-cat B geq G-wcat B geq wcat B geq wcat e geq conil B geq cup-long B$ and furthermore all the inequalities can occur. All the examples are spaces of the form $B = S^qcup_alpha e^n$ where $alphain pi_{n-1} (S^q)$. When B is of this form, we obtain conditions for the category and the weak categories of B to be less than or equal to one of the terms of Hopf invariants of $alpha$. We use these conditions to prove the examples. We then prove the dual theorem concerning the relationships between the invariants cocategory, weak cocategory, nilpotency and Whitehead product length. THEOREM Let A be countable CW-complex, then $cocat A geq wcocat A geq nil A geq W-long A$ and furthermore all the inequalities can occur. The proof is not dual to the first theorem, though the examples we use to show that the inequalities can exist are all spaces with two non-zero homotopy groups. The most interesting of these examples is the space A with 2 non-zero homotopy groups, $mathbb Z$ in dimension 2 and ${mathbb Z}_4$ in dimension 7 with k-invariant $u^4 in H^8(mathbb Z, 2; {mathbb Z}_4)$. This space is not an H-space, but has weak cocategory 1. The condition $wcocat A leq 1$ is equivalent to the fact that d is homotopic to 0 in the fibration $D -d-> A -e-> OmegaSigma A$. In order to show that wcocat A = 1 we have to calculate to cohomology ring of $OmegaSigma K(mathbb Z,2)$. The method we use to do this is the same as that used to calculate the cohomology ring of $OmegaSigma S^{n+1}$ using James' reduced product construction. Finally we show that for the above space A the fibration $Omega A -g-> A^S -f-> A$ has a retraction $ ho$ such that $ hocirc g$ is homotopic to 1 even though A is not an H-space.

This thesis explores the ways in which key holistic thinkers over the course of the last three hundred years have articulated unity between the human subject and objective world. I borrow the term “holism” from the philosopher J. C. Smuts, who coined it in his 1936 work Holism and Evolution, and I use it here in an expanded sense that includes all thinkers in the Western tradition who, like Smuts, have been preoccupied with the question of unity. Although the nature of cosmic unity and the individual’s place within it have been questions for philosophical debate since the classical Greeks of the sixth and fifth centuries BC, from the seventeenth century onwards these questions became largely associated with a series of thinkers who sought to overcome the dualistic separation of subject and object introduced by Galileo, Descartes and others in the mechanistic philosophical tradition of Western thought. My consideration of the holistic tradition includes selected writings by Leibniz, Hegel, Whitehead and Arne Naess, cofounder and key communicator of the deep ecology movement. In my discussion of these authors I observe an emerging pattern that has gradually carried holistic thought away from its traditional dependence on an absolute universal Being as the origin of unity in the world, towards an increasing emphasis on Becoming as the origin of Being. This pattern is confirmed by my broad analyses of Renaissance philosophy and of the Counter-Enlightenment thinkers Vico, Hamann and Herder. It is further confirmed by Naess’ vision of the deep ecology movement, which emphasizes plurality and diversity in the struggle to create more ecologically sustainable forms of human living. The pattern is challenged, however, by my discussions of Heraclitus and of the deep ecology movement, which both exhibit features that also contradict the existence of a definite linear progression “from Being to Becoming.” Insofar as the deep ecology movement recognizes the validity of a broad diversity of philosophical views and premises as grounds for ecological action and decision-making, it is part of a larger movement in contemporary societies that is helping create an open space wherein all perspectives are appreciated as valuable in their own right. This movement seeks to challenge all absolute and hegemonic claims to truth (which in the early twentieth century gave rise to fascism and in our present day continue to inform our views of nature and the self), and, as I suggest, is also contributing to the emergence of an apophatic perspective in our own day that is a precondition for change. / Graduate / 0422 / 0585 / jdesser@uvic.ca

This dissertation examines the problem of coming to terms with the past in post-World War II Germany in the wake of the Holocaust by examining the philosophical critiques of Theodor Adorno and Eric Voegelin. It then extends these critiques into the ongoing discussion of post-Holocaust philosophy and theology, while introducing the speculative philosophy of Alfred North Whitehead as a helpful and appropriate means for continuing metaphysical reflection and perceiving the influence of the past upon the present and future in post-Holocaust discourse. This dissertation suggests, alongside Adorno and Voegelin, that finally coming to terms with the past proves much more dangerous than helpful. Instead, the focus should remain on remembering and reflecting critically upon the deleterious past of the Holocaust in order to avoid forgetfulness or effacement of the past. Whitehead's philosophy provides a metaphysical means for considering how the past remains with us in the present and into the future. Out of this injunction to remember comes a theology of remembrance, which draws heavily from Walter Benjamin's writing on weak messianism and inverse theology. The final focus of the dissertation is the development of a Christian theology of remembrance that requires Christians to rethink theology in light of the Holocaust.

The post-secular event within which we live is occasioned as the limit of the secular project. The secular project meets its limit in attempting to separate a religious private sphere from a public sphere while at the same time repeating as a demand a religious subjectivation of the public sphere: demanding conformity to a simple subjectivity, producing a world of simple subjects through a theologically determined metaphysics of conversion. In this latter demand secularism enforces a simplicity of its subjects and its world. Yet this simplicity cannot be taken up into or as life. To genuinely live and think the post-secular requires, then, not simply a resistance to the secular but a resistance to simplicity, developing ways of becoming otherwise than simply and of producing a world other than that which conforms to a metaphysics of conversion. This dissertation proposes to meet the requirements of the post-secular event by developing a post-secular political ontology drawn from the work of Judith Butler and Alfred North Whitehead. Read through and out of these two philosophers of becoming is a post-secular political ontology that is embedded within a metaphysics of creativity, a metaphysic that is itself already infected by the political. At the intersection of the work of Butler and Whitehead a metaphysic arises that is a systematic discourse of the political. From this metaphysic a political ontology is developed. This political ontology begins with a suspicion of grammar as a suspicion of a subject-predicate form of thought that grounds ontologies of substance. With this suspicion, being is allowed to unfold as its becoming, particularly as a becoming material, so that actuality is a becoming materiality. This is also a relational becoming of feeling, becoming as a process of intensive feeling that can never be finalized for itself, always suffering its own continual downfall. Finally, but without finality, actuality is a becoming of creativity, opened by a divine violence that ruptures history by the possible, leading to a post-secular political ontology of the future.