Cohomological Topics in Group Theory PDF Download

Author: K. W. Gruenberg
Publisher: Springer
ISBN: 3540363033
Category : Mathematics
Languages : en
Pages : 293

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Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 9783540611813
Category : Mathematics
Languages : en
Pages : 236

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Book Description
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: Piotr Pragacz
Publisher: Springer Science & Business Media
ISBN: 3764373423
Category : Mathematics
Languages : en
Pages : 321

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Book Description
The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis

Author: Jürgen Neukirch
Publisher: Springer Science & Business Media
ISBN: 3540378898
Category : Mathematics
Languages : en
Pages : 831

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Book Description
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: Alejandro Adem
Publisher: Springer Science & Business Media
ISBN: 3662062828
Category : Mathematics
Languages : en
Pages : 333

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Book Description
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: Karl W. Gruenberg
Publisher:
ISBN:
Category : Group theory
Languages : en
Pages : 142

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Author: Kenneth S. Brown
Publisher: Springer Science & Business Media
ISBN: 1468493272
Category : Mathematics
Languages : en
Pages : 318

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Book Description
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: Josi A. de Azcárraga
Publisher: Cambridge University Press
ISBN: 9780521597005
Category : Mathematics
Languages : en
Pages : 480

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Book Description
A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.

Author: David Harari
Publisher: Springer Nature
ISBN: 3030439011
Category : Mathematics
Languages : en
Pages : 336

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Book Description
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: Ararat Babakhanian
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 264

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Book Description
This book is intended for students interested in learning the use of cohomology and homology theory in solving problems in group theory. Although cohomology groups of a groups were formally defined in the early 1940s, these groups in low dimensions had been studied earlier as part of the general body of theory of groups. In the last three decades cohomology of groups has played a central role in various branches of mathematics. This book provides readers with the basic tools in cohomology of groups and to illustrate their use in obtaining group theoretic results.