By Nigel Higson

This paintings attracts jointly rules from algebraic topology, sensible research and geometry. it's a instrument - a way of conveying info between those 3 topics - 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 fundamental principles of analytic K-homology and increase a few of its functions. It encompasses a specified creation to the mandatory sensible research, through an exploration of the connections among K-homology and operator idea, 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 publication should still lead the reader to a few crucial notions of up to date examine in geometric useful research.

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