Cohomology Of Finite Groups

Author : Alejandro Adem,R.James Milgram
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 47,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662062821

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Cohomology of Finite Groups by Alejandro Adem,R.James Milgram Pdf

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.

Author : Jon F. Carlson,L. Townsley,Luís Valero-Elizondo,Mucheng Zhang
Publisher : Springer Science & Business Media
Page : 782 pages
File Size : 46,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401702157

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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 : Kenneth S. Brown
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493276

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Cohomology of Groups by Kenneth S. Brown Pdf

Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.

Author : Jürgen Neukirch,Alexander Schmidt,Kay Wingberg
Publisher : Springer Science & Business Media
Page : 831 pages
File Size : 47,8 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9783540378891

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Cohomology of Number Fields by Jürgen Neukirch,Alexander Schmidt,Kay Wingberg Pdf

This second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. In all it is a virtually complete treatment of a vast array of central topics in algebraic number theory. New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields.

Author : D. J. Benson
Publisher : Cambridge University Press
Page : 296 pages
File Size : 50,8 Mb
Release : 1991-08-22
Category : Mathematics
ISBN : 0521636523

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Representations and Cohomology: Volume 2, Cohomology of Groups and Modules by D. J. Benson Pdf

A further introduction to modern developments in the representation theory of finite groups and associative algebras.

Author : C. B. Thomas
Publisher : Cambridge University Press
Page : 0 pages
File Size : 47,5 Mb
Release : 1986
Category : Mathematics
ISBN : 9780521256612

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Characteristic Classes and the Cohomology of Finite Groups by C. B. Thomas Pdf

The purpose of this book is to study the relation between the representation ring of a finite group and its integral cohomology by means of characteristic classes. In this way it is possible to extend the known calculations and prove some general results for the integral cohomology ring of a group G of prime power order. Among the groups considered are those of p-rank less than 3, extra-special p-groups, symmetric groups and linear groups over finite fields. An important tool is the Riemann - Roch formula which provides a relation between the characteristic classes of an induced representation, the classes of the underlying representation and those of the permutation representation of the infinite symmetric group. Dr Thomas also discusses the implications of his work for some arithmetic groups which will interest algebraic number theorists. Dr Thomas assumes the reader has taken basic courses in algebraic topology, group theory and homological algebra, but has included an appendix in which he gives a purely topological proof of the Riemann - Roch formula.

Author : William G. Dwyer,Hans-Werner Henn
Publisher : Birkhäuser
Page : 106 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883566

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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 : Jon Carlson,L. Townsley,Luis Valero-Elizondo
Publisher : Unknown
Page : 796 pages
File Size : 43,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401702160

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

Author : David J. Benson,Srikanth Iyengar,Henning Krause
Publisher : Springer Science & Business Media
Page : 115 pages
File Size : 47,9 Mb
Release : 2011-11-15
Category : Mathematics
ISBN : 9783034802604

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Representations of Finite Groups: Local Cohomology and Support by David J. Benson,Srikanth Iyengar,Henning Krause Pdf

The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas from commutative algebra, cohomology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been Daniel Quillen’s description of the algebraic variety corresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods of algebraic geometry to obtain representation theoretic information. Their work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutative Hopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins’ classification of thick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localizing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approach to address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with ring of operators. The book serves as an introduction to this circle of ideas.

Author : Ari Babakhanian,Queen's University (Kingston, Ont.)
Publisher : Kingston, Ont. : Queen's University
Page : 217 pages
File Size : 40,5 Mb
Release : 1999
Category : Algebra, Homological
ISBN : 0889118388

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Cohomology of Finite Groups by Ari Babakhanian,Queen's University (Kingston, Ont.) Pdf

Author : Leonard Evens
Publisher : Unknown
Page : 0 pages
File Size : 42,6 Mb
Release : 2023
Category : Finite groups
ISBN : 1383025762

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The Cohomology of Groups by Leonard Evens Pdf

This textbook presents an account of the theory of the cohomology ring of a finite group. The aim is to present a modern approach from the point of view of homological algebra. Topics include finite generation theorems, the cohomology of wreath products, norm maps and variety theory.

Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 41,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642591419

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Galois Cohomology by Jean-Pierre Serre Pdf

This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.

Author : David Harari
Publisher : Springer Nature
Page : 336 pages
File Size : 51,8 Mb
Release : 2020-06-24
Category : Mathematics
ISBN : 9783030439019

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Galois Cohomology and Class Field Theory by David Harari Pdf

This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.

Author : Luis Ribes,Pavel Zalesskii
Publisher : Springer Science & Business Media
Page : 441 pages
File Size : 52,7 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9783662040973

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Profinite Groups by Luis Ribes,Pavel Zalesskii Pdf

This self-contained book serves both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. It contains complete and clear proofs for most results, many of which appear here in book form for the first time. Suitable as a basis for courses.

Author : David J. Green
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 45,5 Mb
Release : 2003-11-18
Category : Mathematics
ISBN : 3540203397

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Gröbner Bases and the Computation of Group Cohomology by David J. Green Pdf

This monograph develops the Gröbner basis methods needed to perform efficient state of the art calculations in the cohomology of finite groups. Results obtained include the first counterexample to the conjecture that the ideal of essential classes squares to zero. The context is J. F. Carlson’s minimal resolutions approach to cohomology computations.