Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies the R(infinity) property in the cases where S is either the compact disk D, or the sphere S(2). This means that for any automorphism phi of G, where G is one of the above groups, the number of twisted phi-conjugacy classes is infinite.

Braid groups, mapping class groups, and Torelli groups

This thesis discusses subgroups of mapping class groups of particular surfaces. First, we study the Torelli group, that is, the subgroup of the mapping class group that acts trivially on the first homology. We investigate generators of the Torelli group, and we give an algorithm that factorizes elements of the Torelli group into products of particular generators. Furthermore, we investigate normal closures of powers of standard generators of the mapping class group of a punctured sphere. By using the Jones representation, we prove that in most cases these normal closures have infinite index in the mapping class group. We prove a similar result for the hyperelliptic mapping class group, that is, the group that consists of mapping classes that commute with a fixed hyperelliptic involution. As a corollary, we recover an older theorem of Coxeter (with 2 exceptional cases), which states that the normal closure of the m-th power of standard generators of the braid group has infinite index in the braid group. Finally, we study finite index subgroups of braid groups, namely, congruence subgroups of braid groups. We discuss presentations of these groups and we provide a topological interpretation of their generating sets.

Computation of locally free class groups

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.

The classification and the conjugacy classes of the finite subgroups of the sphere braid groups

Let n >= 3. We classify the finite groups which are realised as subgroups of the sphere braid group B(n)(S(2)). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal finite subgroups of B(n)(S(2)): Z(2(n-1)); the dicyclic groups of order 4n and 4(n - 2); the binary tetrahedral group T*; the binary octahedral group O*; and the binary icosahedral group I(*). We give geometric as well as some explicit algebraic constructions of these groups in B(n)(S(2)) and determine the number of conjugacy classes of such finite subgroups. We also reprove Murasugi`s classification of the torsion elements of B(n)(S(2)) and explain how the finite subgroups of B(n)(S(2)) are related to this classification, as well as to the lower central and derived series of B(n)(S(2)).

Mapping class group e complesso delle curve per superfici di Heegaard

In una 3-varietà chiusa è possibile individuare alcune superfici (dette di Heegaard) tali che, tagliando la 3-varietà lungo una di queste, essa si spezza in due corpi con manici che hanno per bordo tale superficie. La tesi propone alcuni recenti risultati circa l'interazione tra la topologia della 3-varietà, il gruppo di automorfismi delle sue superfici di Heegaard e complessi simpliciali costruiti a partire dalle curve su tali superfici.

Fundamental domains for proper affine actions of Coxeter groups in three dimensions

We study proper actions of groups $G \cong \Z/2\Z \ast \Z/2\Z \ast \Z/2\Z$ on affine space of three real dimensions. Since $G$ is nonsolvable, work of Fried and Goldman implies that it preserves a Lorentzian metric. A subgroup $\Gamma < G$ of index two acts freely, and $\R^3/\Gamma$ is a Margulis spacetime associated to a hyperbolic surface $\Sigma$. When $\Sigma$ is convex cocompact, work of Danciger, Gu{\'e}ritaud, and Kassel shows that the action of $\Gamma$ admits a polyhedral fundamental domain bounded by crooked planes. We consider under what circumstances the action of $G$ also admits a crooked fundamental domain. We show that it is possible to construct actions of $G$ that fail to admit crooked fundamental domains exactly when the extended mapping class group of $\Sigma$ fails to act transitively on the top-dimensional simplices of the arc complex of $\Sigma$. We also provide explicit descriptions of the moduli space of $G$ actions that admit crooked fundamental domains.

Common Bound: The Small Groups of Methodism

The system of small groups John Wesley established to promote a proper life of discipleship in early Methodist converts was, in many respects, the strength of the Methodist movement. Those who responded to Wesley’s initial invitation to “flee the wrath to come” were organized into large gatherings called “societies,” which were then subdivided into smaller bands, class meetings, select societies, and penitent bands. The smaller groups gave Wesley the opportunity, through a system of appointed leaders, to keep track of the spiritual progress of every member in his movement, which grew to tens of thousands by the time of his death in 1791. As Methodism shifted from renewal movement to institutional church in the nineteenth century, however, growth slowed, and participation in such groups declined rapidly. By the early twentieth century, classes and bands were virtually extinct in every sector of Methodism save the African-American tradition. In recent years, scholars in various sectors of the Wesleyan tradition, particularly David Lowes Watson and Kevin Watson, have called for a recovery of these small groups for purposes of renewal in the church. There is no consensus, however, concerning what exactly contributed to the vitality of these groups during Wesley’s ministry.

Over the last century, sociological studies of group dynamics have revealed three common traits that are crucial to highly functioning groups: interdependence created by the existence of a common goal, interaction among group members that is “promotive” or cooperative in nature, and high levels of feedback associated with personal responsibility and individual accountability. All three of these were prevalent in the early Methodist groups. Interdependence existed around a shared goal, which for Wesley and the Methodists was holiness. That interdependence was cooperative in nature; individuals experienced the empowering grace of God as they each pursued the goal in the company of fellow pilgrims. Finally, the groups existed for purposes of feedback and accountability as individuals took responsibility both for themselves and others as they progressed together toward the goal of holy living. Wesley seemed to instinctively understand the essential nature of each of these characteristics in maintaining the vitality of the movement when he spoke of the importance of preserving the “doctrine, spirit and discipline” of early Methodism. Analysis of some of the present-day attempts to restore Wesley’s groups reveals frequent neglect to one or more of these three components. Perhaps most critical to recovering the vitality of the early Methodist groups will be reclaiming the goal of sanctification and coming to a consensus on what its pursuit means in the present day.

Cultivating Subjectivities: The Class Politics of Convivial Labor in the Interstitial Spaces of Neoliberal Neglect

Thesis (Ph.D.)--University of Washington, 2016-08

Survey of Lifestyle, Attitudes and Nutrition in Ireland. Mental Health and Social Well-being Report

SĹN 2007: Older People, Loneliness and Social Support to Mental HealthSĹN, the national Survey of Lifestyle, Attitudes and Nutrition, shows that most Irish adults have a reasonably high level of positive mental health. It is the largest national survey on positive and negative mental health and social well-being in the Irish adult population.��One finding highlights the significance of loneliness and social support to mental health. Finding reveal that 14% of respondents reported being often lonely in the last four weeks, with women, older people and respondents in lower social class groups reporting high levels of loneliness. The SĹN report indicates that being widowed and not being in paid employment are the strongest overall predictors of loneliness. Respondents who are widowed are about five times more likely to feel lonely than those who are married or cohabiting, while 17% of respondents aged 65 and over report being often lonely.��SLAN 2007 highlights the significance of loneliness and social support to mental health. It proposes community-based interventions, including community development approaches and strategies to promote community involvement as a way to tackle such social and health inequities at local level. The report also highlights the importance of implementing the recommendations of the policy document A Vision for Change. It says that protection and promotion of the future health and well-being of the Irish population requires the implementation of effective cross-sectoral policies that will help create and maintain a mentally healthy society, with consequent health, economic and social benefits for all.����SLAN is commissioned by the Department of Health and Children and involved face-to-face interviews with 10,364 respondents aged 18 years and over.��

Asymptotics of number fields and the Cohen-Lenstra heuristics

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen-Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

Empreendendo a aprendizagem: uma proposta de co-participação em sala de aula

Esta pesquisa pretendeu gerar pistas para situações do dia-a-dia dos alunos do curso de Administração, na disciplina de Psicologia, co-responsabilizando-os por sua produção e solução dos conflitos da classe. Nossa investigação centrou-se no grupo de discussão constituído por representantes (rodiziados) dos pequenos grupos da classe, apoiados pelo professor para discutir: a) dúvidas temáticas; b) sugestão para conflitos ocorridos intragrupos e intergrupos. Indagamos se: essa metodologia favoreceu a cooperação e a criatividade intergrupos e intragrupos? Como recursos auxiliares, utilizamos o sistema de monitoria/didática dos emergentes/devolutiva do processo grupal/confecção de textos pelos alunos.

Atividade de ensino de ciências: representação de alunos do ensino fundamental - NPI/UFPA

O presente estudo objetivou analisar as representações sociais das atividades de ensino de ciências de alunos da oitava série, de ambos os sexos, do ensino fundamental do Núcleo Pedagógico Integrado/NPI-Escola de Aplicação de Educação Básica da Universidade Federal do Pará, do ano de 2003/4. Além de investigar os conteúdos partilhados pelos alunos e identificar as contribuições das representações sociais para as atividades de ensino de ciências na prática do ensino de educação em ciências. O princípio que orientou essa investigação foi a Teoria das Representações Sociais elaborada por Serge Moscovic em 1961. A Teoria das Representações Sociais é definida por seu criador como o conjunto de conceitos, proposições e explicações originado na vida cotidiana no curso de comunicações interpessoais. Elas são equivalentes, em nossa sociedade, aos mitos e sistemas de crenças das sociedades tradicionais; podem também ser vistas como a versão contemporânea do senso comum. Esse estudo se fundamentou especialmente na Teoria do Núcleo Central proposta por Abric(1994) e colaboradores, que vem sendo desenvolvida ao longo dos anos: Todos os elementos da representação são hierarquizados e situam-se em torno de um núcleo central, constituído de um ou de alguns elementos que dão à representação o seu significado. O desenvolvimento do trabalho incluiu a caracterização dos sujeitos pertencentes a quatro turmas do período letivo de 2004 num total de 119 sujeitos respondentes. Foi realizada anteriormente, a aplicação de um questionário-piloto que procurou testar e validar as questões nele elaboradas. Tinha como principal objetivo identificar as representações sociais desses alunos a partir da questão: Quais são as representações sociais das atividades de ensino de ciências que os alunos de oitava série possuem? Utilizando a Teoria do Núcleo Central, foi possível perceber as imagens e sentidos na relação das atividades de ensino de ciências e as representações dos alunos, principalmente com a expressão meio ambiente como sua maior manifestação. Além disso, foi percebida a relação dos elementos do universo através de seus componentes, tendo o ser humano como seu elemento integrador. As representações (imagens e sentidos) percebidas sugerem um conjunto de reações positivas e negativas com vistas à transformação do ensino praticado em sala de aula. Os sujeitos propõem um refazer da prática dos membros da comunidade escolar, especialmente à prática dos professores. Esperamos que os resultados deste estudo sejam relevantes para o aprimoramento dos objetivos da educação científica, pois trazem reflexões importantes para o decisivo processo de melhoria da prática docente.

Motivación, flow e intención de práctica físico-deportiva en estudiantes de educación física de España y Latinoamérica

A pesar de los innegables beneficios físicos y psicosociales que la práctica de actividad física tiene para la población en las últimas décadas se observa un importante descenso en el nivel de práctica de actividad física durante la adolescencia. La Educación Física (EF) es una asignatura presente en las primeras etapas educativas de los currículums de todos los países y supone para la población infantil y adolescente, durante el periodo de escolarización obligatoria, un entorno de contacto cotidiano con la actividad física y deportiva lo que explica el creciente interés que existe por investigar en este contexto y extraer conclusiones que puedan ayudar a revertir el proceso de progresivo abandono de la práctica en estas edades. El presente trabajo se centra en un periodo, la adolescencia, especialmente sensible al abandono de la práctica de actividad física. Apoyándonos en tres de los marcos teóricos más importantes de los últimos años - Teoría de Metas de Logro, Teoría de la Autodeterminación y Teoría del Flow - hemos realizado un diseño con tres estudios complementarios que nos permitan avanzar en el conocimiento de las variables que afectan a esta realidad. En el primero de los estudios, en el que participaron 3990 estudiantes de EF de España, Argentina, Colombia y Ecuador con edades comprendidas entre 12 y 18 años, se fijaron como objetivos el establecimiento de perfiles motivacionales en estudiantes de EF considerando las orientaciones motivacionales, la motivación intrínseca y el flow disposicional; la comprobación de la posible estabilidad de los perfiles establecidos en cuatro países diferentes; y el análisis de la relación entre los perfiles motivacionales establecidos con la práctica de actividad física realizada en la actualidad y la intención de ser activo en el futuro. Los resultados revelaron la existencia de tres perfiles motivacionales en los estudiantes: perfil de motivación baja-moderada, perfil de motivación de alta motivación con bajo ego y perfil de alta motivación. Se encontraron similitudes en los perfiles motivacionales obtenidos en los cuatro países analizados, sugiriéndose la posibilidad de que la lengua materna compartida pueda ser una variable de influencia en la existencia de patrones conductuales similares. La orientación al ego resultó ser un elemento diferenciador en la relación de los dos perfiles que mostraron niveles más altos de motivación intrínseca, flow disposicional y orientación a la tarea con las variables de práctica. Mayores niveles de orientación al ego determinaron mayores valores de práctica e intención de práctica. En el segundo estudio, en el que participaron 365 estudiantes de EF de España, Argentina y Colombia con edades comprendidas entre 12 y 16 años, se testó un modelo explicativo de la intención de ser físicamente activo en el futuro en estudiantes de EF poco motivados introduciendo el flow disposicional como variable explicativa junto a las orientaciones motivacionales y la motivación intrínseca. El modelo de ecuaciones estructurales testado muestra que tanto la orientación al ego como la orientación a la tarea y la motivación intrínseca predijeron el flow disposicional. No se encontró un efecto significativo de la orientación a la tarea sobre la motivación intrínseca, ni de esta sobre la intención de práctica de AFD en el futuro. El flow disposicional resultó ser un mediador entre ambas orientaciones motivacionales y dicha intención, adquiriendo un papel relevante en la predicción de la intención de realizar actividad física en el futuro en los sujetos con poca motivación hacia la clase de EF. En el último estudio, con una muestra de 53 estudiantes de EF pertenecientes a dos clases de segundo curso de ESO con edades comprendidas entre 13 y 15 años, se analizó el efecto de una intervención de apoyo a las NPB sobre la satisfacción de las mismas, la motivación intrínseca, la disposición a experimentar flow y la intención de ser físicamente activo en el futuro; estudiándose también el efecto de la misma sobre ciertas variables presentes en el proceso de enseñanza-aprendizaje tales como la diversión, el aprendizaje y el gusto hacia el contenido y la metodología empleada. La intervención resultó efectiva en la mejora de todas las variables motivacionales analizadas a excepción de la satisfacción de la necesidad de relaciones sociales, variable que podría ser más difícilmente modificable en tanto que los grupos de clase suelen permanecer estables a lo largo de esta etapa educativa. Los alumnos de la condición experimental presentaron niveles más elevados de diversión, aprendizaje y gusto hacia el contenido y la metodología empleada. ABSTRACT Despite the undeniable physical and psychological benefits that physical activity has on health, a significant drop in the level of physical activity during adolescence has been observed over the last few decades. Physical education (PE) is present in the early stages of educational curricula of all countries, creating an environment in which children and adolescents can maintain daily contact with sport and physical activity during the period of compulsory education. There is thus a growing interest in research within this context, helping to draw conclusions aimed at reversing the progressive decline of physical activity in this age bracket. The work presented here focuses on adolescence – a period particularly sensitive when faced with declining rates of physical activity. Relying on three of the most important recent theoretical frameworks – Achievement Goal Theory, Self-Determination Theory and Flow Theory – we have carried out a design using three complementary studies that allow us to advance the understanding of variables affecting this reality. The first two studies employ a correlational methodology while the third follows a quasi-experimental design. The objectives of the first study, with the participation of 3990 PE students aged 12 to 18 from Spain, Argentina, Colombia and Ecuador, were: a) to establish motivational profiles in physical education students taking into consideration motivational orientations, intrinsic motivation and dispositional flow; b) to check the possible stability of the established profiles in the four countries; and c) to analyze the relationship between motivational profiles and both current levels of physical activity and intention to be physically active in the future. Results revealed the existence of three motivational profiles: low-moderate motivation profile, high motivation and low ego profile and high motivation profile. Similarities were found across the four countries, which presents the possibility that sharing the same mother tongue might influence the existence of similar behavioral patterns. Amongst the profiles that showed the highest levels of intrinsic motivation, dispositional flow and task orientation with practice variables, ego orientation became apparent as a differentiating element. Higher levels of ego orientation correlated with higher levels both in current level of physical activity and intention to be physically active in the future. In the second study, with the participation of 365 PE students aged 12 to 16 from Spain, Argentina and Colombia, an explanatory model of the intention to be physically active within the low-moderate motivation profile was tested, including dispositional flow as an influence variable together with motivational orientations and intrinsic motivation. The structural model equation in the low-moderate motivation profile shows some differences with respect to findings of similar studies using heterogeneous samples in motivational profiles. It was found that ego orientation, task orientation and intrinsic motivation predicted dispositional flow. No significant effects of task orientation on intrinsic motivation, or of intrinsic motivation on intention to be physically active in the future were found. Dispositional flow emerged as a mediator between both motivational orientations and intention, acquiring an important role in the prediction of future intentions to be physically active in adolescents who show low levels of motivation towards physical education. In the last of the three studies, with the participation of 53 PE students drawn from two classes in the second year of secondary education aged 13 to 15, the effect of an intervention to support basic psychological needs was tested against the satisfaction of these needs, intrinsic motivation, disposition to experience flow and intention to be physically active in the future. Alongside this, the aforementioned intervention was tested on certain variables present in the teaching-learning process such as fun, learning and taste for the activity and methodology. Supportive intervention was effective in improving all the motivational variables, except for the satisfaction of the relatedness variable, which may be more difficult to modify as class groups tend to remain stable throughout this educational state. Students in the experimental condition showed higher levels of fun, learning and taste for the content and methodology.

On T-Semisimplicity of Iwasawa Modules and Some Computations with Z3-Extensions

Thesis (Ph.D.)--University of Washington, 2016-08