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. The purpose 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, coarse geometry, 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 material included here has never previously appeared in book form.

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Bibliographic Details

Title: Analytic K-Homology
Publisher: Oxford University Press, GB
Publication Date: 2000
Language: English
ISBN 10: 0198511760
ISBN 13: 9780198511762
Binding: Hardback
Edition: Illustrated.
Condition: New
Dimensions: 23.4 centimeters width by 15.6 centimeters height by 2.38 centimeters depth
Weight: 720 grams

About this title

Synopsis

This text acquaints the reader with the essential ideas of analytic K-homology and develops 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, coarse geometry, index theory, and assembly maps, including a detailed treatment of the Atiyah-Singer Index Theorem. Beginning with the rudiments of C*-algebra theory, it leads the reader into some of the central notions of contemporary research in geometric functional analysis.

About the Author

Nigel Higson is at Pennsylvania State University. John Roe is at Pennsylvania State University.

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