By Nigel Higson
This paintings attracts jointly rules from algebraic topology, practical research and geometry. it's a instrument - a way 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 booklet is to acquaint the reader with the fundamental principles of analytic K-homology and strengthen a few of its purposes. It incorporates a specified creation to the mandatory useful research, by way of an exploration of the connections among K-homology and operator concept, coarse geometry, index conception, and meeting maps, together with a close remedy of the Atiyah-Singer Index Theorem. starting with the rudiments of C* - algebra conception, the ebook may still lead the reader to a few significant notions of latest study in geometric useful research.
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