Geometry And Cohomology In Group Theory

Author : Peter H. Kropholler,Graham A. Niblo,Ralph Stöhr
Publisher : Cambridge University Press
Page : 332 pages
File Size : 49,6 Mb
Release : 1998-05-14
Category : Mathematics
ISBN : 9780521635561

Get Book

Geometry and Cohomology in Group Theory by Peter H. Kropholler,Graham A. Niblo,Ralph Stöhr Pdf

This volume reflects the fruitful connections between group theory and topology. It contains articles on cohomology, representation theory, geometric and combinatorial group theory. Some of the world's best known figures in this very active area of mathematics have made contributions, including substantial articles from Ol'shanskii, Mikhajlovskii, Carlson, Benson, Linnell, Wilson and Grigorchuk, which will be valuable reference works for some years to come. Pure mathematicians working in the fields of algebra, topology, and their interactions, will find this book of great interest.

Author : D.J. Collins,R.I. Grigorchuk,P.F. Kurchanov,H. Zieschang
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 44,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642580130

Get Book

Algebra VII by D.J. Collins,R.I. Grigorchuk,P.F. Kurchanov,H. Zieschang Pdf

From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996

Author : Jon F. Carlson,L. Townsley,Luís Valero-Elizondo,Mucheng Zhang
Publisher : Springer Science & Business Media
Page : 782 pages
File Size : 42,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401702157

Get Book

Cohomology Rings of Finite Groups by Jon F. Carlson,L. Townsley,Luís Valero-Elizondo,Mucheng Zhang Pdf

Group cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num ber theory, and it grew into an integral component of algebraic topology. In the last thirty years, group cohomology has developed a powerful con nection with finite group representations. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in teractions with representation theory involve cohomology rings and the geometry of spectra over these rings. It is this connection to represen tation theory that we take as our primary motivation for this book. The book consists of two separate pieces. Chronologically, the first part was the computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64. The ideas and the programs for the calculations were developed over the last 10 years. Several new features were added over the course of that time. We had originally planned to include only a brief introduction to the calculations. However, we were persuaded to produce a more substantial text that would include in greater detail the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the com putations. We have gathered together many of the results and ideas that are the focus of the calculations from throughout the mathematical literature.

Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 249 pages
File Size : 42,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475756739

Get Book

Local Fields by Jean-Pierre Serre Pdf

The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray.

Author : Serge Lang
Publisher : Springer
Page : 231 pages
File Size : 52,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540683377

Get Book

Topics in Cohomology of Groups by Serge Lang Pdf

The book is a mostly translated reprint of a report on cohomology of groups from the 1950s and 1960s, originally written as background for the Artin-Tate notes on class field theory, following the cohomological approach. This report was first published (in French) by Benjamin. For this new English edition, the author added Tate's local duality, written up from letters which John Tate sent to Lang in 1958 - 1959. Except for this last item, which requires more substantial background in algebraic geometry and especially abelian varieties, the rest of the book is basically elementary, depending only on standard homological algebra at the level of first year graduate students.

Author : Jon Carlson,L. Townsley,Luis Valero-Elizondo
Publisher : Unknown
Page : 796 pages
File Size : 49,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401702160

Get Book

Cohomology Rings of Finite Groups by Jon Carlson,L. Townsley,Luis Valero-Elizondo Pdf

Author : William G. Dwyer,Hans-Werner Henn
Publisher : Birkhäuser
Page : 106 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883566

Get Book

Homotopy Theoretic Methods in Group Cohomology by William G. Dwyer,Hans-Werner Henn Pdf

This book consists essentially of notes which were written for an Advanced Course on Classifying Spaces and Cohomology of Groups. The course took place at the Centre de Recerca Mathematica (CRM) in Bellaterra from May 27 to June 2, 1998 and was part of an emphasis semester on Algebraic Topology. It consisted of two parallel series of 6 lectures of 90 minutes each and was intended as an introduction to new homotopy theoretic methods in group cohomology. The first part of the book is concerned with methods of decomposing the classifying space of a finite group into pieces made of classifying spaces of appropriate subgroups. Such decompositions have been used with great success in the last 10-15 years in the homotopy theory of classifying spaces of compact Lie groups and p-compact groups in the sense of Dwyer and Wilkerson. For simplicity the emphasis here is on finite groups and on homological properties of various decompositions known as centralizer resp. normalizer resp. subgroup decomposition. A unified treatment of the various decompositions is given and the relations between them are explored. This is preceeded by a detailed discussion of basic notions such as classifying spaces, simplicial complexes and homotopy colimits.

Author : Torsten Wedhorn
Publisher : Springer
Page : 366 pages
File Size : 51,6 Mb
Release : 2016-07-25
Category : Mathematics
ISBN : 9783658106331

Get Book

Manifolds, Sheaves, and Cohomology by Torsten Wedhorn Pdf

This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.

Author : Mladen Bestvina,Michah Sageev,Karen Vogtmann
Publisher : American Mathematical Soc.
Page : 417 pages
File Size : 51,9 Mb
Release : 2014-12-24
Category : Mathematics
ISBN : 9781470412272

Get Book

Geometric Group Theory by Mladen Bestvina,Michah Sageev,Karen Vogtmann Pdf

Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups. This book is a valuable resource for graduate students and researchers interested in geometric group theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Author : Cornelia Druţu,Michael Kapovich
Publisher : American Mathematical Soc.
Page : 819 pages
File Size : 46,6 Mb
Release : 2018-03-28
Category : Geometric group theory
ISBN : 9781470411046

Get Book

Geometric Group Theory by Cornelia Druţu,Michael Kapovich Pdf

The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.

Author : Roberto Frigerio
Publisher : American Mathematical Soc.
Page : 193 pages
File Size : 45,7 Mb
Release : 2017-11-21
Category : Algebra, Homological
ISBN : 9781470441463

Get Book

Bounded Cohomology of Discrete Groups by Roberto Frigerio Pdf

The theory of bounded cohomology, introduced by Gromov in the late 1980s, has had powerful applications in geometric group theory and the geometry and topology of manifolds, and has been the topic of active research continuing to this day. This monograph provides a unified, self-contained introduction to the theory and its applications, making it accessible to a student who has completed a first course in algebraic topology and manifold theory. The book can be used as a source for research projects for master's students, as a thorough introduction to the field for graduate students, and as a valuable landmark text for researchers, providing both the details of the theory of bounded cohomology and links of the theory to other closely related areas. The first part of the book is devoted to settling the fundamental definitions of the theory, and to proving some of the (by now classical) results on low-dimensional bounded cohomology and on bounded cohomology of topological spaces. The second part describes applications of the theory to the study of the simplicial volume of manifolds, to the classification of circle actions, to the analysis of maximal representations of surface groups, and to the study of flat vector bundles with a particular emphasis on the possible use of bounded cohomology in relation with the Chern conjecture. Each chapter ends with a discussion of further reading that puts the presented results in a broader context.

Author : Burt Totaro
Publisher : Cambridge University Press
Page : 245 pages
File Size : 43,8 Mb
Release : 2014-06-26
Category : Mathematics
ISBN : 9781107015777

Get Book

Group Cohomology and Algebraic Cycles by Burt Totaro Pdf

This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.

Author : S. Buoncristiano,Colin Patrick Rourke,Brian Joseph Sanderson
Publisher : Cambridge University Press
Page : 157 pages
File Size : 40,5 Mb
Release : 1976-04
Category : Mathematics
ISBN : 9780521209403

Get Book

A Geometric Approach to Homology Theory by S. Buoncristiano,Colin Patrick Rourke,Brian Joseph Sanderson Pdf

The purpose of these notes is to give a geometrical treatment of generalized homology and cohomology theories. The central idea is that of a 'mock bundle', which is the geometric cocycle of a general cobordism theory, and the main new result is that any homology theory is a generalized bordism theory. The book will interest mathematicians working in both piecewise linear and algebraic topology especially homology theory as it reaches the frontiers of current research in the topic. The book is also suitable for use as a graduate course in homology theory.

Author : Shubham Dwivedi,Jonathan Herman,Lisa C. Jeffrey,Theo van den Hurk
Publisher : Springer Nature
Page : 132 pages
File Size : 49,9 Mb
Release : 2019-09-23
Category : Mathematics
ISBN : 9783030272272

Get Book

Hamiltonian Group Actions and Equivariant Cohomology by Shubham Dwivedi,Jonathan Herman,Lisa C. Jeffrey,Theo van den Hurk Pdf

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.

Author : Peter H. Kropholler,Ian J. Leary,Conchita Martínez-Pérez,Brita E. A. Nucinkis
Publisher : Cambridge University Press
Page : 277 pages
File Size : 53,9 Mb
Release : 2018
Category : Mathematics
ISBN : 9781316623220

Get Book

Geometric and Cohomological Group Theory by Peter H. Kropholler,Ian J. Leary,Conchita Martínez-Pérez,Brita E. A. Nucinkis Pdf

Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.