Transformation Groups and Algebraic K-Theory

Transformation Groups and Algebraic K-Theory
Title Transformation Groups and Algebraic K-Theory PDF eBook
Author Wolfgang Lück
Publisher Springer
Pages 455
Release 2006-11-14
Genre Mathematics
ISBN 3540468277

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The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the theory of transformation groups sometimes hard to find in the literature, are collected here (Chapter I) for the benefit of graduate students. Chapters II and III contain advanced new material of interest to researchers working in transformation groups, algebraic K-theory or related fields.

The $K$-book

The $K$-book
Title The $K$-book PDF eBook
Author Charles A. Weibel
Publisher American Mathematical Soc.
Pages 634
Release 2013-06-13
Genre Mathematics
ISBN 0821891324

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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

K-theory of Forms

K-theory of Forms
Title K-theory of Forms PDF eBook
Author Anthony Bak
Publisher Princeton University Press
Pages 284
Release 1981-11-21
Genre Mathematics
ISBN 9780691082752

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The description for this book, K-Theory of Forms. (AM-98), Volume 98, will be forthcoming.

Space Mappings with Bounded Distortion

Space Mappings with Bounded Distortion
Title Space Mappings with Bounded Distortion PDF eBook
Author I_Uri_ Grigor_evich Reshetni_ak
Publisher American Mathematical Soc.
Pages 384
Release 1989-12-31
Genre Mathematics
ISBN 9780821898215

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This book is intended for researchers and students concerned with questions in analysis and function theory. The author provides an exposition of the main results obtained in recent years by Soviet and other mathematicians in the theory of mappings with bounded distortion, an active direction in contemporary mathematics. The mathematical tools presented can be applied to a broad spectrum of problems that go beyond the context of the main topic of investigation. For a number of questions in the theory of partial differential equations and the theory of functions with generalized derivatives, this is the first time they have appeared in an internationally distributed monograph.

The Local Structure of Algebraic K-Theory

The Local Structure of Algebraic K-Theory
Title The Local Structure of Algebraic K-Theory PDF eBook
Author Bjørn Ian Dundas
Publisher Springer Science & Business Media
Pages 447
Release 2012-09-06
Genre Mathematics
ISBN 1447143930

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Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.

Introduction to Algebraic K-theory

Introduction to Algebraic K-theory
Title Introduction to Algebraic K-theory PDF eBook
Author John Willard Milnor
Publisher Princeton University Press
Pages 204
Release 1971
Genre Mathematics
ISBN 9780691081014

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Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

Cohomological Methods in Transformation Groups

Cohomological Methods in Transformation Groups
Title Cohomological Methods in Transformation Groups PDF eBook
Author C. Allday
Publisher Cambridge University Press
Pages 486
Release 1993-07
Genre Mathematics
ISBN 0521350220

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This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.