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.
Complex Topological K-Theory
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'... the presentation is very nice and the book can be strongly recommended.' European Mathematical Society Newsletter
Book 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, every aspect of the topic is covered, and exercises are included at the end of each chapter.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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fiberwise norm, smooth idempotent, homotopic idempotents, compact pair, external multiplication, external tensor product, bundle homomorphism, bundle isomorphism, abelian monoid, alternate picture, vector space homomorphism, smooth vector bundle, splitting principle, monoid homomorphism, simple tensors, vector bundles, vector space basis, invariant polynomial Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Proposition, Proof Take, Proof Choose, Proof Suppose, Proof Follows, Proof Fix, Relative K-theory, Proof Write, K-theory Definition, Proof Imbed Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
fiberwise norm, smooth idempotent, homotopic idempotents, compact pair, external multiplication, external tensor product, bundle homomorphism, bundle isomorphism, abelian monoid, alternate picture, vector space homomorphism, smooth vector bundle, splitting principle, monoid homomorphism, simple tensors, vector bundles, vector space basis, invariant polynomial Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Proposition, Proof Take, Proof Choose, Proof Suppose, Proof Follows, Proof Fix, Relative K-theory, Proof Write, K-theory Definition, Proof Imbed Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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