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Complex Topological K-Theory

ISBN-10: 0521856345

ISBN-13: 9780521856348

Edition: 2008

Authors: Efton Park

List price: $105.00
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Description:

Topological K-theory is a key tool in topology, differential geometry and index theory, yet this is the first contemporary introduction for graduate students new to the subject. No background in algebraic topology is assumed; the reader need only have taken the standard first courses in real analysis, abstract algebra, and point-set topology. The book begins with a detailed discussion of vector bundles and related algebraic notions, followed by the definition of K-theory and proofs of the most important theorems in the subject, such as the Bott periodicity theorem and the Thom isomorphism theorem. The multiplicative structure of K-theory and the Adams operations are also discussed and the final chapter details the construction and computation of characteristic classes. With every important aspect of the topic covered, and exercises at the end of each chapter, this is the definitive book for a first course in topological K-theory.
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Book details

List price: $105.00
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 3/13/2008
Binding: Hardcover
Pages: 218
Size: 6.00" wide x 9.00" long x 0.50" tall
Weight: 0.880
Language: English

Efton Park is a Professor in the Department of Mathematics at Texas Christian University.

Preface
Preliminaries
Complex inner product spaces
Matrices of continuous functions
Invertibles
Idempotents
Vector bundles
Abelian monoids and the Grothendieck completion
Vect(X) vs. Idem(C(X))
Some homological algebra
A very brief introduction to category theory
Notes
Exercises
K-theory
Definition of K<sup>0</sup>(X)
Relative K-theory
Invertibles and K<sup>-1</sup>
Connecting K<sup>0</sup> and K<sup>-1</sup>
Reduced K-theory
K-theory of locally compact topological spaces
Bott periodicity
Computation of some K groups
Cohomology theories and K-theory
Notes
Exercises
Additional structure
Mayer-Vietoris
Tensor products
Multiplicative structures
An alternate picture of relative K<sup>0</sup>
The exterior algebra
Thom isomorphism theorem
The splitting principle
Operations
The Hopf invariant
Notes
Exercises
Characteristic classes
De Rham cohomology
Invariant polynomials
Characteristic classes
The Chern character
Notes
Exercises
References
Symbol index
Subject index