Hyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on the "Big Monster," i.e., on Thurston 's hyperbolization theorem, which has not only completely changes the landscape of 3-dimensinal topology and Kleinian group theory but is one of the central results of 3-dimensional topology.

The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index. It should serve as an ideal graduate course/seminar text or as a comprehensive reference.

toComplexRe ectionGroups and Their Braid Groups 123 Michel Broue Universite Paris Diderot Paris 7 UFR de Mathematiques 175 Rue du Chevaleret 75013 Paris France broue@math. jussieu. fr ISBN: 978-3-642-11174-7 e-ISBN: 978-3-642-11175-4 DOI: 10. 1007/978-3-642-11175-4 Springer Heidelberg Dordrecht London New York Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2009943837 Mathematics Subject Classi cation (2000): 20, 13, 16, 55 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, speci cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on micro lm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of aspeci c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover illustration: c Anouk Grinberg Cover design: SPi Publisher Services Printed on acid-free paper springer. com Preface Weyl groups are ?nite groups acting as re?ection groups on rational vector spaces. It iswellknownthat theserationalre?ectiongroupsappearas"ske- tons" of many important mathematical objects: algebraic groups, Hecke algebras, Artin-Tits braid groups, etc."

This book is a collection of articles, some introductory, some extended surveys, and some containing previously unpublished research, on a range of topics linking infinite permutation group theory and model theory. Topics covered include: oligomorphic permutation groups and omega-categorical structures; totally categorical structures and covers; automorphism groups of recursively saturated structures; Jordan groups; Hrushovski's constructions of pseudoplanes; permutation groups of finite Morley rank; applications of permutation group theory to models of set theory without the axiom of choice. There are introductory chapters by the editors on general model theory and permutation theory, recursively saturated structures, and on groups of finite Morley rank. The book is almost self-contained, and should be useful to both a beginning postgraduate student meeting the subject for the first time, and to an active researcher from either of the two main fields looking for an overview of the subject.

Trust is a crucial facet of social functioning that feeds into our relationships with individuals, groups, and organizations. The Psychology of Interpersonal Trust: Theory and Research examines existing theories, frameworks, and models of trust as well as the methods and designs for examining it. To fully examine how interpersonal trust impacts our lives, Rotenberg reviews the many essential topics trust relates to, including close relationships, trust games, behavioural trust, and trust development. Designed to encourage researchers to recognize the links between different approaches to trust, this book begins with an overview of the different approaches to interpersonal trust and a description of the methods used to investigate it. Following on from this, each chapter introduces a new subtopic or context, including lying, adjustment, socialization, social media, politics, and health. Each subtopic begins with a short monologue (to provide a personal perspective) and covers basic theory and research. Rotenberg's applied focus demonstrates the relevance of interpersonal trust and highlights the issues and problems people face in contemporary society. This is essential reading for students, researchers, and academics in social psychology, especially those with a specific interest in the concept of trust.

Ce travail en deux volumes donne la preuve de la stabilisation de la formule des trace tordue. Stabiliser la formule des traces tordue est la methode la plus puissante connue actuellement pour comprendre l'action naturelle du groupe des points adeliques d'un groupe reductif, tordue par un automorphisme, sur les formes automorphes de carre integrable de ce groupe. Cette comprehension se fait en reduisant le probleme, suivant les idees de Langlands, a des groupes plus petits munis d'un certain nombre de donnees auxiliaires; c'est ce que l'on appelle les donnees endoscopiques. L'analogue non tordu a ete resolu par J. Arthur et dans ce livre on suit la strategie de celui-ci. Publier ce travail sous forme de livre permet de le rendre le plus complet possible. Les auteurs ont repris la theorie de l'endoscopie tordue developpee par R. Kottwitz et D. Shelstad et par J.-P. Labesse. Ils donnent tous les arguments des demonstrations meme si nombre d'entre eux se tr ouvent deja dans les travaux d'Arthur concernant le cas de la formule des traces non tordue. Ce travail permet de rendre inconditionnelle la classification que J. Arthur a donnee des formes automorphes de carre integrable pour les groupes classiques quasi-deployes, c'etait pour les auteurs une des principales motivations pour l'ecrire. Cette partie contient les preuves de la stabilisation geometrique et de la partie spectrale en particulier de la partie discrete de ce terme, ce qui est le point d'aboutissement de ce sujet.

The aim of this monograph is to give an overview of various classes of in?ni- dimensional Lie groups and their applications, mostly in Hamiltonian - chanics, ?uid dynamics, integrable systems, and complex geometry. We have chosen to present the unifying ideas of the theory by concentrating on speci?c typesandexamplesofin?nite-dimensionalLiegroups. Ofcourse, theselection of the topics is largely in?uenced by the taste of the authors, but we hope thatthisselectioniswideenoughtodescribevariousphenomenaarisinginthe geometry of in?nite-dimensional Lie groups and to convince the reader that they are appealing objects to study from both purely mathematical and more applied points of view. This book can be thought of as complementary to the existing more algebraic treatments, in particular, those covering the str- ture and representation theory of in?nite-dimensional Lie algebras, as well as to more analytic ones developing calculus on in?nite-dimensional manifolds. This monograph originated from advanced graduate courses and mi- courses on in?nite-dimensional groups and gauge theory given by the ?rst author at the University of Toronto, at the CIRM in Marseille, and at the Ecole Polytechnique in Paris in 2001-2004. It is based on various classical and recentresultsthathaveshapedthisnewlyemergedpartofin?nite-dimensional geometry and group theory. Our intention was to make the book concise, relatively self-contained, and useful in a graduate course. For this reason, throughout the text, we have included a large number of problems, ranging from simple exercises to open questions

Drawing on psychological and sociological perspectives as well as quantitative and qualitative data, Identity and Interethnic Marriage in the United States considers the ways the self and social identity are linked to the dynamics of interethnic marriage. Bringing together the classic theoretical contributions of George Herbert Mead, Erving Goffman, and Erik Erikson with contemporary research on ethnic identity inspired by Jean Phinney, this book argues that the self and social identity-especially ethnic identity-are reflected in individuals' complex journey from singlehood to interethnic marriage within the United States.

A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series, which consists of the subgroups determined by the augmentation powers, is a challenging task. This monograph presents an exposition of different methods for investigating this relationship. In addition to group theorists, the results are also of interest to topologists and number theorists. The approach is mainly combinatorial and homological. A novel feature is an exposition of simplicial methods for the study of problems in group theory.

This is the softcover reprint of the English translation of Bourbaki's text Groupes et Algebres de Lie, Chapters 7 to 9. It completes the previously published translations of Chapters 1 to 3 (3-540-64242-0) and 4 to 6 (978-3-540-69171-6) by covering the structure and representation theory of semi-simple Lie algebras and compact Lie groups. Chapter 7 deals with Cartan subalgebras of Lie algebras, regular elements and conjugacy theorems. Chapter 8 begins with the structure of split semi-simple Lie algebras and their root systems. It goes on to describe the finite-dimensional modules for such algebras, including the character formula of Hermann Weyl. It concludes with the theory of Chevalley orders. Chapter 9 is devoted to the theory of compact Lie groups, beginning with a discussion of their maximal tori, root systems and Weyl groups. It goes on to describe the representation theory of compact Lie groups, including the application of integration to establish Weyl's formula in this context. The chapter concludes with a discussion of the actions of compact Lie groups on manifolds. The nine chapters together form the most comprehensive text available on the theory of Lie groups and Lie algebras.

What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen. We learn how the bechamel in a lasagna can be a lot like the number five, and why making a good custard proves that math is easy but life is hard. At the heart of it all is Cheng's work on category theory, a cutting-edge "mathematics of mathematics," that is about figuring out how math works. Combined with her infectious enthusiasm for cooking and true zest for life, Cheng's perspective on math is a funny journey through a vast territory no popular book on math has explored before. So, what is math? Let's look for the answer in the kitchen.

People interact and perform in group settings in all areas of life. Organizations and businesses are increasingly structuring work around groups and teams. Every day, we work in groups such as families, friendship groups, societies and sports teams, to make decisions and plans, solve problems, perform physical tasks, generate creative ideas, and more. Group Performance outlines the current state of social psychological theories and findings concerning the performance of groups. It explores the basic theories surrounding group interaction and development and investigates how groups affect their members. Bernard A. Nijstad discusses these issues in relation to the many different tasks that groups may perform, including physical tasks, idea generation and brainstorming, decision-making, problem-solving, and making judgments and estimates. Finally, the book closes with an in-depth discussion of teamwork and the context in which groups interact and perform. Offering an integrated approach, with particular emphasis on the interplay between group members, the group task, interaction processes and context, this book provides a state-of-the-art overview of social psychological theory and research. It will be highly valuable to undergraduates, graduates and researchers in social psychology, organizational behavior and business.

Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. It explores the analytic behavior of these functions together with an investigation of functional equations. The book examines many important examples of zeta functions, providing an important database of explicit examples and methods for calculation.

This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.

This is an elementary introduction to the representation theory of real and complex matrix groups. The text is written for students in mathematics and physics who have a good knowledge of differential/integral calculus and linear algebra and are familiar with basic facts from algebra, number theory and complex analysis. The goal is to present the fundamental concepts of representation theory, to describe the connection between them, and to explain some of their background. The focus is on groups which are of particular interest for applications in physics and number theory (e.g. Gell-Mann's eightfold way and theta functions, automorphic forms). The reader finds a large variety of examples which are presented in detail and from different points of view.

Ethnocentrism works to reinvigorate the study of ethnocentrism by reconceptualising ethnocentrism as a social, psychological, and attitudinal construct. Using a broad, multidisciplinary approach to ethnocentrism, the book integrates literature from disciplines such as psychology, political science, sociology, anthropology, biology, and marketing studies to create a novel reorganisation of the existing literature, its origins, and its outcomes. Empirical research throughout serves to comprehensively measure the six dimensions of ethnocentrism-devotion, group cohesion, preference, superiority, purity, and exploitativeness-and show how they factor into causes and consequences of ethnocentrism, including personality, values, morality, demographics, political ideology, social factors, prejudice, discrimination, and nationalism. Ethnocentrism is fascinating reading for scholars, researchers, and students in psychology, sociology, and political science.

Coming Home Your Way offers college and university students returning from an education-abroad experience a wealth of pertinent information, opportunities for meaningful reflection, and practical guidance on making the most of their time abroad. Grounded in research and addressing an array of aspects of education abroad - including intercultural communication, changing relationships, and career impact - Coming Home Your Way will be an invaluable tool for any student planning, experiencing, or returning from a stay abroad. Drawing from theory and research from multiple disciplines, and real-world experiences of students who have studied abroad, the volume addresses key themes critical to understanding reentry, including individual differences in taking in experience, communication patterns and approaches, the reentry transition, the nature of relationships in reentry, bridging reentry and career, and more. Within each chapter are opportunities for self-reflection that allow readers to integrate the ideas presented into their own experience. Compelling short fictional accounts add flavor and detail that bring theory to life. Coming Home Your Way provides a window into the complex experience of intercultural reentry. Reentry from an education-abroad experience can be a period of intense growth, and can feel disruptive and confusing while it's happening. The authors explain and explore these complexities in a conversational style that will engage students, and with the rigor expected by their instructors. Like no other book currently on the market, Coming Home Your Way will give college and university students insight into the challenges and intercultural opportunities that reentry offers.

Operational Quantum Theory II is a distinguished work on quantum theory at an advanced algebraic level. The classically oriented hierarchy with objects such as particles as the primary focus, and interactions of the objects as the secondary focus is reversed with the operational interactions as basic quantum structures. Quantum theory, specifically relativistic quantum field theory is developed the theory of Lie group and Lie algebra operations acting on both finite and infinite dimensional vector spaces. This book deals with the operational concepts of relativistic space time, the Lorentz and Poincare group operations and their unitary representations, particularly the elementary articles. Also discussed are eigenvalues and invariants for non-compact operations in general as well as the harmonic analysis of noncompact nonabelian Lie groups and their homogeneous spaces. In addition to the operational formulation of the standard model of particle interactions, an attempt is made to understand the particle spectrum with the masses and coupling constants as the invariants and normalizations of a tangent representation structure of a an homogeneous space time model. Operational Quantum Theory II aims to understand more deeply on an operational basis what one is working with in relativistic quantum field theory, but also suggests new solutions to previously unsolved problems.

Present a systematic treatment of completely regular semigroups, from introductory to research level, comprised of preliminaries on lattices, semigroups, varieties, and complete regularity; congruences and relations on the congruence lattice; and varieties of completely regular semigroups through kernals, and traces of congruences and Malcev products.

Ce travail en deux volumes donne la preuve de la stabilisation de la formule des trace tordue. Stabiliser la formule des traces tordue est la methode la plus puissante connue actuellement pour comprendre l'action naturelle du groupe des points adeliques d'un groupe reductif, tordue par un automorphisme, sur les formes automorphes de carre integrable de ce groupe. Cette comprehension se fait en reduisant le probleme, suivant les idees de Langlands, a des groupes plus petits munis d'un certain nombre de donnees auxiliaires; c'est ce que l'on appelle les donnees endoscopiques. L'analogue non tordu a ete resolu par J. Arthur et dans ce livre on suit la strategie de celui-ci. Publier ce travail sous forme de livre permet de le rendre le plus complet possible. Les auteurs ont repris la theorie de l'endoscopie tordue developpee par R. Kottwitz et D. Shelstad et par J.-P. Labesse. Ils donnent tous les arguments des demonstrations meme si nombre d'entre eux se trouvent deja dans les travaux d'Arthur concernant le cas de la formule des traces non tordue. Ce travail permet de rendre inconditionnelle la classification que J. Arthur a donnee des formes automorphes de carre integrable pour les groupes classiques quasi-deployes, c'etait pour les auteurs une des principales motivations pour l'ecrire. Cette premiere partie comprend les chapitres preparatoires (I-V).

Recent developments are covered

Contains over 100 figures and 250 exercises

Includes complete proofs

The volume is a collection of refereed research papers on infinite dimensional groups and manifolds in mathematics and quantum physics. Topics covered are: new classes of Lie groups of mappings, the Burgers equation, the Chern--Weil construction in infinite dimensions, the hamiltonian approach to quantum field theory, and different aspects of large N limits ranging from approximation methods in quantum mechanics to modular forms and string/gauge theory duality. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of important themes of research at the forefront of mathematics and theoretical physics.

This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.

H.S.M. Coxeter is one of the world's best-known mathematicians who wrote several papers and books on geometry, algebra and topology, and finite mathematics. This book is being published in conjunction with the 50th anniversary of the Canadian Mathematical Society and it is a collection of 26 papers written by Dr. Coxeter.

Finite Coxeter groups and related structures arise naturally in several branches of mathematics, for example, Lie algebras or theory of knots and links. This is the first book which develops the character theory of finite Coxeter groups and Iwahori-Hecke algebras in a systematic way, ranging from classical results to recent developments.

An important monograph summarising the development of a classification system fo finite p-groups.