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Groups And Related Topics

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Problems On Mapping Class Groups And Related Topics

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Author : Benson Farb
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-09-12

Problems On Mapping Class Groups And Related Topics written by Benson Farb and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-12 with Mathematics categories.

The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.

Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics

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Author : Aaron Wootton
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-03

Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics written by Aaron Wootton and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-03 with Mathematics categories.

Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.

Topics In The Theory Of Group Presentations

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Author : D. L. Johnson
language : en
Publisher: Cambridge University Press
Release Date : 1980-07-31

Topics In The Theory Of Group Presentations written by D. L. Johnson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-07-31 with Mathematics categories.

These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises have been added and the treatment of a number of topics has been improved and expanded. In addition, there are new chapters on the triangle groups, small cancellation theory and groups from topology. The connections between the theory of group presentations and other areas of mathematics are emphasized throughout. The book can be used as a text for beginning research students and, for specialists in other fields, serves as an introduction both to the subject and to more advanced treatises.

Representation Theory Of Solvable Lie Groups And Related Topics

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Author : Ali Baklouti
language : en
Publisher:
Release Date : 2021

Representation Theory Of Solvable Lie Groups And Related Topics written by Ali Baklouti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

The purpose of the book is to discuss the latest advances in the theory of unitary representations and harmonic analysis for solvable Lie groups. The orbit method created by Kirillov is the most powerful tool to build the ground frame of these theories. Many problems are studied in the nilpotent case, but several obstacles arise when encompassing exponentially solvable settings. The book offers the most recent solutions to a number of open questions that arose over the last decades, presents the newest related results, and offers an alluring platform for progressing in this research area. The book is unique in the literature for which the readership extends to graduate students, researchers, and beginners in the fields of harmonic analysis on solvable homogeneous spaces.

Topics In Geometric Group Theory

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Author : Pierre de la Harpe
language : en
Publisher: University of Chicago Press
Release Date : 2000-10-15

Topics In Geometric Group Theory written by Pierre de la Harpe and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-15 with Education categories.

In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.

Probabilistic Analysis And Related Topics

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Author : A. T. Bharucha-Reid
language : en
Publisher: Elsevier
Release Date : 2014-05-10

Probabilistic Analysis And Related Topics written by A. T. Bharucha-Reid and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Probabilistic Analysis and Related Topics, Volume 2 focuses on the integrability, continuity, and differentiability of random functions, as well as functional analysis, measure theory, operator theory, and numerical analysis. The selection first offers information on the optimal control of stochastic systems and Gleason measures. Discussions focus on convergence of Gleason measures, random Gleason measures, orthogonally scattered Gleason measures, existence of optimal controls without feedback, random necessary conditions, and Gleason measures in tensor products. The text then elaborates on an introduction to nonstandard analysis and hyperfinite probability theory, including applications to stochastic processes, conversion from nonstandard to standard measure spaces, and an introduction to nonstandard analysis. The text examines stochastic matrices, ergodic Markov chains, and measures on semigroups, as well as limit theorems for convolution products of probability measures on completely simple semigroups; ergodicity of Markov chains and probability measures on semigroups; and limits of convolutions in groups and semigroups. The selection is a dependable source of data for mathematicians and researchers interested in the general theory of random functions.

Introduction To Affine Group Schemes

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Author : W.C. Waterhouse
language : en
Publisher: Springer Science & Business Media
Release Date : 1979-11-13

Introduction To Affine Group Schemes written by W.C. Waterhouse and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-11-13 with Mathematics categories.

Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme.

How To Create And Sustain Groups That Thrive

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Author : Ann Steiner, Ph.D.
language : en
Publisher: Routledge
Release Date : 2020-05-25

How To Create And Sustain Groups That Thrive written by Ann Steiner, Ph.D. and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-25 with Psychology categories.

How to Create and Sustain Groups That Thrive is an accessible manual for group leaders of all kinds, from psychotherapy groups to discussion groups. This thoroughly updated third edition of the author’s popular group psychotherapy guide provides a wealth of tools for starting and maintaining groups, including sample group agreements, a screening and preparation system, and an innovative collaborative goal setting system. The book also discusses the importance of online ‘netiquette’ as well as an overview of diversity and inclusion concepts in group work, offering a range of modifiable leadership and facilitation interventions that can be tailored to meet the needs of specific groups. Specifically designed to help both seasoned group therapists and clinicians who find themselves leading groups, How to Create and Sustain Groups That Thrive is an easy-to-use, fully practical resource for a variety of mental health professionals.

Topics In Geometric Group Theory

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Author : Pierre de la Harpe
language : en
Publisher: University of Chicago Press
Release Date : 2000-09-15

The Emerald Handbook Of Group And Team Communication Research

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Author : Stephenson J. Beck
language : en
Publisher: Emerald Group Publishing
Release Date : 2021-11-05

The Emerald Handbook Of Group And Team Communication Research written by Stephenson J. Beck and has been published by Emerald Group Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-05 with Business & Economics categories.

This volume considers the current research of group communication scholars, provides an overview of major foci in the discipline, and points toward possible trajectories for future scholarship. It establishes group communication’s central role within research on human behaviour and fosters an identity for group communication researchers.

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