Complex Topological K-Theory
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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.
List price: $105.00
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 3/13/2008
Size: 6.00" wide x 9.00" long x 0.50" tall
Efton Park is a Professor in the Department of Mathematics at Texas Christian University.
|Complex inner product spaces|
|Matrices of continuous functions|
|Abelian monoids and the Grothendieck completion|
|Vect(X) vs. Idem(C(X))|
|Some homological algebra|
|A very brief introduction to category theory|
|Definition of K<sup>0</sup>(X)|
|Invertibles and K<sup>-1</sup>|
|Connecting K<sup>0</sup> and K<sup>-1</sup>|
|K-theory of locally compact topological spaces|
|Computation of some K groups|
|Cohomology theories and K-theory|
|An alternate picture of relative K<sup>0</sup>|
|The exterior algebra|
|Thom isomorphism theorem|
|The splitting principle|
|The Hopf invariant|
|De Rham cohomology|
|The Chern character|