By Nigel Higson
This paintings attracts jointly principles from algebraic topology, useful research and geometry. it's a device - a method of conveying details between those 3 matters - and it's been used with good fortune to find theorems throughout a large span of arithmetic. the aim of this e-book is to acquaint the reader with the basic principles of analytic K-homology and boost a few of its functions. It encompasses a particular advent to the mandatory useful research, by means of an exploration of the connections among K-homology and operator concept, coarse geometry, index idea, and meeting maps, together with a close therapy of the Atiyah-Singer Index Theorem. starting with the rudiments of C* - algebra thought, the booklet may still lead the reader to a few critical notions of up to date study in geometric useful research.
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