The theory of discrete groups acting on finite dimensional Euclidean open balls by hyperbolic isometries was borne around the end of 19th century within the works of Fuchs, Klein and Poincaré. We develop the theory of discrete groups acting by hyperbolic isometries on the open unit ball of an infinite dimensional separable Hilbert space. We present our investigations on the geometry of limit sets at the sphere at infinity with an attempt to highlight the differences between the finite and infinite dimensional theories. We discuss the existence of fixed points of isometries and the classification of isometries. Various notions of discreteness that were equivalent in finite dimensions, no longer turn out to be in our setting. In this regard, the robust notion of strong discreteness is introduced and we study limit sets for properly discontinuous actions. We go on to prove a generalization of the Bishop-Jones formula for strongly discrete groups, equating the Hausdorff dimension of the radial limit set with the Poincaré exponent of the group. We end with a short discussion on conformal measures and their relation with Hausdorff and packing measures on the limit set.

Thesis (Dr. rer. nat.)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2002. / Includes bibliographical references.

Thesis (Ph.D.) - University of St Andrews, January 2009.

We study hyperbolic structures on the compression body C with genus 2 positive boundary and genus 1 negative boundary. We consider individual hyperbolic structures as well as special regions in the space of all such hyperbolic structures. We use some properties of the boundary hyperbolic structures on C to establish an interesting property of cusp shapes of tunnel number one manifolds. This extends a result of Nimershiem in [26] to the class of tunnel number one manifolds. We also establish convergence results on the geometry of compression bodies. This extends the work of Ito in [13] from the punctured-torus case to the compression body case.

In this paper, we present techniques for proving a group to be non-left-orderable or a unique product group. These methods involve the existence of a mapping from the group to R which obeys a left-multiplication criterion. By determining the existence or non-existence of such a mapping, the desired information about the group can be concluded. As examples, we apply this technique to groups of transformations in hyperbolic 2- and 3- space, and Fibonacci groups. / Master of Science

This thesis investigates the structure and properties of hyperbolic 3-manifold groups (particularly knot and link groups) and arithmetic Kleinian groups. In Chapter 2, we establish a stronger version of a conjecture of A. Reid and others in the arithmetic case: if two elements of equal trace (e.g., conjugate elements) generate an arithmetic two-bridge knot or link group, then the elements are parabolic (and hence peripheral). In Chapter 3, we identify all Kleinian groups that can be generated by two elements for which equality holds in Jørgensen’s Inequality in two cases: torsion-free Kleinian groups and non-cocompact arithmetic Kleinian groups. / text

Abstract A Kleinian Analysis of Organisations: Implications for Employee Health and Well-Being. This dissertation considers research that was conducted into the impact of organisational style of operation upon the health and well-being of individual employees. A Kleinian analysis of organisations, from a psychoanalytic perspective, highlights the defining characteristics of different organisations within the study. The intent of the thesis is to argue that the different types of organisations impact upon the health and well-being of their employees. Six organisations were studied using both qualitative and quantitative methods. Extensive interviews were conducted with 120 employees from those organisations. A Kleinian Analysis Questionnaire and a Kleinian Analysis Rating Scale (new psychoanalytic techniques aimed at promoting dialogue with employees) assisted in the analysis and positioning of the organisations. The findings suggested that organisations can be distinguished in Kleinian terms and that these differences produce a range of health effects for employees. In the qualitative parts of this research extensive discussions took place with the employees of organisations considered to be in either the Depressive position or the Paranoid – Schizoid positions. Using the Kleinian Analysis Questionnaire (KAQ), a great deal was revealed about the emotional lives of their organisations and the impact of these realities on their own individual emotional lives and on their mental and physical health. Organisational employee assistance programs (EAPs) were considered in terms of how support was extended to employees within the studied organisations and how the efficacy and utilization of EAPs were affected by organisational classification of either Depressive or Paranoid-Schizoid. A range of quantitative measures were employed in the study and included the broad health measures SF-36, the Satisfaction With Life Scale (SWLS), the Schedule for the Evaluation of Individual Quality of Life - Direct Weighting (SEIQoL-DW) and the Work Environment Scale (WES). Employees in the Depressive organisations described their workplaces as open, encouraging, creative, flexible and democratic in process. They described how the stated values and mission statements of their organisations were consistent with their own personal values and how their work as described by Gabriel (2002) enhanced their sense of self esteem and self image. There were abundant examples of their organisations providing support, described in psychoanalytic terms as ‘containment’. The quantitative results, in part, supported the qualitative results by demonstrating that the employees of Depressive organisations had a better rate of recovery from psychological issues arising from personal and workplace matters. In contrast, employees from Paranoid – Schizoid organisations described their workplaces as defensive, blaming, scapegoating, rigid and concrete, where organisational behaviour was often inconsistent with the organisation’s stated values and mission statements. They described some of the competitive activity as inconsistent with their own personal values and at times giving rise to anxiety. This discord had reflections on the emotional health of individuals. This was borne out in the quantitative aspects of the study which also found that the mental health of individuals and their rate of recovery from psychological issues were adversely affected by the lack of ‘containment’ afforded to them by their organisations. The results strongly demonstrated the value of EAPs as mechanisms of support for employees and revealed differences in the impact upon health and well-being of employees between the two Kleinian organisational types in addition to differences in the levels of utilization and involvement. Keywords: Kleinian Analysis; Health Implications; Employee Assistance Programs; Containment Australian and New Zealand Standard Research Classifications (ANZSRC): 150305:50%; 150311:25%; 179999:25%

This explorative qualitative research investigates whether there is a difference in the symbolic meanings between the bulimic’s behaviour of purposefully expelling food versus the anorexic’s deprivation of food by administering the Thematic Apperceptive Test, as well as, conducting in-depth, semi-structured individual interviews with two bulimic women, two anorexic women of the restrictive sub-type and one anorexic woman of the binge-eating/ purging sub-type, whose ages ranged from twenty-one to thirty-five years of age. Both the conscious and unconscious themes that emerge from their stated relationship with food and their TAT responses are explored, with particular interest being focused on whether the symbolic meaning of food is in essence a “symbolic equation” for an object, specifically the mother and parental couple. The concept of “symbolic equation” is explored analytically from a Kleinian perspective to ascertain whether it is not food, per se that the anorexic is depriving herself of or that the bulimic suddenly and uncontrollably ingests, but then rapidly and violently expels. On the contrary, it appears that the refusal to introject or the ambivalent battle between introjection and expulsion of food is used as a disguise for the underlying conflictual object relation/s. The modified version of the Bellak Scoring System (1986) was used to analyse their TAT responses in order to elicit the themes that represent their internal worlds and object relations. Individual thematic content analysis was conducted on each interview transcript separately, and then a comparative analysis performed to explore commonalities and differences across the transcripts and TAT responses amongst the three anorexic women as a group and the bulimic women as a separate group. After which, the two different eating disorder groups were compared to explore both their differences and similarities. The findings suggest that a variety of conscious and unconscious motives might best be understood within the historical context of each participant’s early development and family dynamics. It appears that the anorexic is unconsciously motivated, at least partly, by her desire to repudiate any experience of dependency, separateness, loss, frustration, envy, fear, guilt and helplessness. Conversely, the bulimic appears to be motivated, at least partly, by the repetitive magical quest to restore a ‘good’ self-object bond and to stifle her destructiveness. Nonetheless, underlying both the anorexic’s and the bulimic’s illness is an ambivalent struggle with internalising a gainful and durable link to an object, which can in some way be permitted to be ‘good’. This appears to have its origin in the mother-daughter relationship, father-daughter relationship, parental couple, as well as, the triangular space between the mother-daughter-father link. / Dissertation (MA)--University of Pretoria, 2008. / Psychology / unrestricted

The mystery surrounding serial homicide is the apparent lack of motive for the murder. No extrinsic motive such as robbery, financial gain, passion or revenge exists, as there usually is in the case of other murders. Serial homicide is a serious, worldwide problem that has received a large amount of media attention, but only a relatively small amount of scientifically based research exists on this phenomenon. Since the 1970s various models such as the psychosocial theory model, learning theory, the motivational, fantasy, neurological theory, psychiatric, post-modern, feminist and the paranormal/demonological models were used to explain the phenomenon of serial homicide. The researcher, however, states that these models do not satisfactorily address the intrapsychic/object relation development of the serial killers personality. The structure of the research project consists of analysis of the background information of two serial killers which was gathered from one semi-structured personal interview, psychometric testing (Thematic Apperception Test, Test of Object Relations and the Picture Test of Separation and Individuation) as well as from relevant literary sources. The information was interpreted using the selected psychoanalytic theory of Sigmund Freund and the object relation theory of Melanie Klein and the data was then analysed, interpreted and tested against the following research questions: “What is the intrapsychic origin of serial homicide?”; “What is the parent-child relationship like?”; “How does the parent-child relationship influence the object relations of the serial killer?”; “How does the parental relationship influence the serial killer’s interpersonal relationships?”. These questions determine the specific internalised factors that may have contributed to the eventual development of a serial killer’s personality. The research method that is employed is a qualitative, exploratory case study method. A qualitative study was selected due to the fact that there are currently not enough incarcerated serial killers in South Africa and from those incarcerated serial killers only two were willing to participate in the research. The case study method was selected because it deals with contemporary events, multiple data sources may be used and the findings can be generalised to other case studies. Data gathering was done by psychometric testing (TAT, PTSI and TOR), a semi-structured interview and other biographical information on the subjects. The data was analysed by the descriptive-dialogic case study method. The data integration method that was selected is the data integration method of the descriptive-dialogic case study method. The data was discussed in relation to the already developed theories. This implies that parallels were drawn between the processed information and the theories. Similarities and differences between the two case studies were discussed and a general overview of the intrapsychic structure of the serial killer was stated. / Dissertation (MA (Psychology))--University of Pretoria, 2006. / Psychology / unrestricted