Analytic K-Homology

Hardcover | October 15, 2000

byNigel Higson, John Roe

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Analytic K-homology draws together ideas from algebraic topology, functional analysis and geometry. It is a tool - a means of conveying information among these three subjects - and it has been used with specacular success to discover remarkable theorems across a wide span of mathematics. Thepurpose of this book is to acquaint the reader with the essential ideas of analytic K-homology and develop some of its applications. It includes a detailed introduction to the necessary functional analysis, followed by an exploration of the connections between K-homology and operator theory, coarsegeometry, index theory, and assembly maps, including a detailed treatment of the Atiyah-Singer Index Theorem. Beginning with the rudiments of C* - algebra theory, the book will lead the reader to some central notions of contemporary research in geometric functional analysis. Much of the materialincluded here has never previously appeared in book form.

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From the Publisher

Analytic K-homology draws together ideas from algebraic topology, functional analysis and geometry. It is a tool - a means of conveying information among these three subjects - and it has been used with specacular success to discover remarkable theorems across a wide span of mathematics. Thepurpose of this book is to acquaint the rea...

Nigel Higson is at Pennsylvania State University. John Roe is at Pennsylvania State University.
Format:HardcoverPublished:October 15, 2000Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198511760

ISBN - 13:9780198511762

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"The book gives a well-written introduction to the essential ideas of analytic K-homology and develops some of its applications."--Mathematical Reviews