Complex Topological K-Theory

Name: Complex Topological K-Theory
Price: 86.97 USD
Availability: InStock
ISBN: 9780521856348

ISBN-10: 0521856345

ISBN-13: 9780521856348

Edition: 2008

Authors: Efton Park

List price: $116.00

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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…

Book details

List price: $116.00
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 3/13/2008
Binding: Hardcover
Pages: 218
Size: 6.18" wide x 9.17" long x 0.47" tall
Weight: 0.946
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