Complex topological K-theory

By:

Park, Efton

Material type: Book

BookSeries: Cambridge studies in advanced mathematics ; 111Publication details: Cambridge: Cambridge University Press, 2008.Description: x, 208p. : ill. ; hb, 23 cmISBN:

9780521856348

Subject(s):

DDC classification:

514.23 PAR

Summary: 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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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	514.23 PAR (Browse shelf(Opens below))	1	Available		030081

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Previous	514.224 KAU Knots and physics	514.23 GIL Central Simple algebras and Galois cohomology	514.23 HIG Analytic k homology	514.23 PAR Complex topological K-theory	514.23 TUL Introductory lectures on equivariant cohomology	514.23 VAI Cohomology and differential forms	514.24 BAR Foundations of stable homotopy theory	Next

Includes bibliographical references and index.

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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