By Nigel Higson

This paintings attracts jointly principles from algebraic topology, sensible research and geometry. it's a instrument - a method of conveying details between those 3 matters - and it's been used with luck to find theorems throughout a large span of arithmetic. the aim of this publication is to acquaint the reader with the basic principles of analytic K-homology and increase a few of its functions. It contains a particular advent to the required sensible research, via an exploration of the connections among K-homology and operator conception, coarse geometry, index concept, and meeting maps, together with an in depth therapy of the Atiyah-Singer Index Theorem. starting with the rudiments of C* - algebra conception, the ebook may still lead the reader to a couple significant notions of latest study in geometric useful research.

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