Author: Lizhen JiPublisher: International Press of Boston
ISBN: 9781571461445
Category : Cohomology operations
Languages : en
Pages : 0
Book Description
Cohomology of Groups and Algebraic K-theory --
Cohomology of Groups and Algebraic K-theory
Author: Lizhen JiPublisher: International Press of Boston
ISBN: 9781571461445
Category : Cohomology operations
Languages : en
Pages : 0
Book Description
Cohomology of Groups and Algebraic K-theory --
Cohomology of Groups
Author: Kenneth S. BrownPublisher: Springer Science & Business Media
ISBN: 1468493272
Category : Mathematics
Languages : en
Pages : 318
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.
The $K$-book
Author: Charles A. WeibelPublisher: American Mathematical Soc.
ISBN: 0821891324
Category : Mathematics
Languages : en
Pages : 634
Book Description
Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr
Higher Algebraic K-Theory: An Overview
Author: Emilio Lluis-PueblaPublisher: Springer
ISBN: 3540466398
Category : Mathematics
Languages : en
Pages : 172
Book Description
This book is a general introduction to Higher Algebraic K-groups of rings and algebraic varieties, which were first defined by Quillen at the beginning of the 70's. These K-groups happen to be useful in many different fields, including topology, algebraic geometry, algebra and number theory. The goal of this volume is to provide graduate students, teachers and researchers with basic definitions, concepts and results, and to give a sampling of current directions of research. Written by five specialists of different parts of the subject, each set of lectures reflects the particular perspective ofits author. As such, this volume can serve as a primer (if not as a technical basic textbook) for mathematicians from many different fields of interest.
Cohomology of Finite Groups
Author: Alejandro AdemPublisher: Springer Science & Business Media
ISBN: 3662062828
Category : Mathematics
Languages : en
Pages : 333
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.
Representations of Algebraic Groups
Author: Jens Carsten JantzenPublisher: American Mathematical Soc.
ISBN: 082184377X
Category : Mathematics
Languages : en
Pages : 594
Book Description
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Group Cohomology and Algebraic Cycles
Author: Burt TotaroPublisher: Cambridge University Press
ISBN: 1107015774
Category : Mathematics
Languages : en
Pages : 245
Book Description
This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.
Algebraic K-Theory and Its Applications
Author: Jonathan RosenbergPublisher: Springer Science & Business Media
ISBN: 1461243149
Category : Mathematics
Languages : en
Pages : 404
Book Description
Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
K-Theory
Author: Max KaroubiPublisher: Springer Science & Business Media
ISBN: 3540798900
Category : Mathematics
Languages : en
Pages : 337
Book Description
From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory. The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".
Handbook of K-Theory
Author: Eric FriedlanderPublisher: Springer Science & Business Media
ISBN: 354023019X
Category : Mathematics
Languages : en
Pages : 1148
Book Description
This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.