Group Representations

Group Representations PDF

Author: Representations Summer Research Institute on Cohomology (and Actions of Finite Groups (1996 : University of Washington, Seattle))

Publisher:

Published: 1997

Total Pages: 532

ISBN-13: 9780821806586

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Group Representations: Cohomology, Group Actions and Topology

Group Representations: Cohomology, Group Actions and Topology PDF

Author: Alejandro Adem

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 549

ISBN-13: 0821806580

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This volume combines contributions in topology and representation theory that reflect the increasingly vigorous interactions between these areas. Topics such as group theory, homotopy theory, cohomology of groups, and modular representations are covered. All papers have been carefully refereed and offer lasting value.

Cohomology of Finite Groups

Cohomology of Finite Groups PDF

Author: Alejandro Adem

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 333

ISBN-13: 3662062828

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The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important new fields in mathematics, like homological algebra and algebraic K-theory. This is the first book to deal comprehensively with the cohomology of finite groups: it introduces the most important and useful algebraic and topological techniques, and describes the interplay of the subject with those of homotopy theory, representation theory and group actions. The combination of theory and examples, together with the techniques for computing the cohomology of important classes of groups including symmetric groups, alternating groups, finite groups of Lie type, and some of the sporadic simple groups, enable readers to acquire an in-depth understanding of group cohomology and its extensive applications.

Group Actions on Manifolds

Group Actions on Manifolds PDF

Author: Reinhard Schultz

Publisher: American Mathematical Soc.

Published: 1985

Total Pages: 586

ISBN-13: 0821850385

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Presents an understanding of the sorts of problems one studies in group actions and the methods used to study such problems. This book features articles based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado.

Hamiltonian Group Actions and Equivariant Cohomology

Hamiltonian Group Actions and Equivariant Cohomology PDF

Author: Shubham Dwivedi

Publisher: Springer Nature

Published: 2019-09-23

Total Pages: 132

ISBN-13: 3030272273

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This monograph could be used for a graduate course on symplectic geometry as well as for independent study. The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.

Topology and Geometric Group Theory

Topology and Geometric Group Theory PDF

Author: Michael W. Davis

Publisher: Springer

Published: 2016-09-14

Total Pages: 174

ISBN-13: 3319436740

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This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.

Geometry, Rigidity, and Group Actions

Geometry, Rigidity, and Group Actions PDF

Author: Robert J Zimmer

Publisher: University of Chicago Press

Published: 2011-04-15

Total Pages: 600

ISBN-13: 0226237907

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The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others. The papers in Geometry, Rigidity, and Group Actions explore the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties. In some cases, the dynamics of the possible group actions are the principal focus of inquiry. In other cases, the dynamics of group actions are a tool for proving theorems about algebra, geometry, or topology. This volume contains surveys of some of the main directions in the field, as well as research articles on topics of current interest.

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