Analytic K-Homology (Oxford Mathematical Monographs) 1st Edition by Nigel Higson (PDF)

Description

This work 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 success to discover 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 should lead the reader to some central notions of contemporary research in geometric functional analysis.

User’s Reviews

Editorial Reviews: Review “The book gives a well-written introduction to the essential ideas of analytic K-homology and develops some of its applications.”–Mathematical Reviews About the Author Nigel Higson is at Pennsylvania State University. John Roe is at Pennsylvania State University.

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