[PDF] Cohomology Of Finite Groups eBook

Author : Alejandro Adem
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 41,29 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 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.

Author : Kenneth S. Brown
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 20,16 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1468493272

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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 : Jon F. Carlson
Publisher : Springer Science & Business Media
Page : 782 pages
File Size : 31,55 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 9401702152

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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 : William G. Dwyer
Publisher : Birkhäuser
Page : 106 pages
File Size : 28,25 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034883560

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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 : D. J. Benson
Publisher : Cambridge University Press
Page : 296 pages
File Size : 25,42 MB
Release : 1991-08-22
Category : Mathematics
ISBN : 9780521636520

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

Author : Burt Totaro
Publisher : Cambridge University Press
Page : 245 pages
File Size : 13,54 MB
Release : 2014-06-26
Category : Mathematics
ISBN : 1107015774

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

Author : Jürgen Neukirch
Publisher : Springer Science & Business Media
Page : 831 pages
File Size : 39,37 MB
Release : 2013-09-26
Category : Mathematics
ISBN : 3540378898

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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 : Leonard Evens
Publisher :
Page : 0 pages
File Size : 42,66 MB
Release : 2023
Category : Finite groups
ISBN : 9781383025767

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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 : David J. Benson
Publisher : Springer Science & Business Media
Page : 115 pages
File Size : 27,61 MB
Release : 2011-11-15
Category : Mathematics
ISBN : 3034802609

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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 : David Harari
Publisher : Springer Nature
Page : 336 pages
File Size : 24,83 MB
Release : 2020-06-24
Category : Mathematics
ISBN : 3030439011

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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.