Description
This book is about analytic K-homology, which is a tool that can be used to connect ideas from algebraic topology, functional analysis, and geometry. It is intended for graduate students and researchers in geometric analysis, and it should lead the reader to some central notions of contemporary research in geometric functional analysis.
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 This book is intended for graduate students, researchers in geometric analysis and professional mathematicians in other areas (such as topology) who want to explore some of the connections made in the book between their work and analytic K- homology. Review: ... this is a very nice book that will interest specialists from several branches of mathematics and be attractive for postgraduate students. EMS
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