Analytic K-HomologyOUP Oxford, 07.12.2000 - 424 Seiten Analytic K-homology 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 specacular success to discover remarkable 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 will lead the reader to some central notions of contemporary research in geometric functional analysis. Much of the material included here has never previously appeared in book form. |
Inhalt
Index Theory and Extensions | 29 |
Completely Positive Maps | 55 |
KTheory | 85 |
Duality Theory | 123 |
Coarse Geometry and KHomology | 141 |
The BrownDouglasFillmore Theorem | 167 |
Kasparovs KHomology | 199 |
The Kasparov Product | 239 |
Elliptic Differential Operators | 269 |
Index Theory | 305 |
Higher Index Theory | 347 |
Appendix A Gradings | 377 |
Appendix B Real KHomology | 387 |
| 401 | |
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Analytic K-homology Nigel Higson,John Roe,Both Professors of Maths John Roe Keine Leseprobe verfügbar - 2000 |
Häufige Begriffe und Wortgruppen
algebra algebraic topology argument associated assume boundary map bounded C*-algebra called Chapter closed coarse structure commutative compact operators completely completely positive connected consider construction continuous controlled corresponding cover defined Definition Definition Let denote determines diagram Dirac operator direct sum domain element elliptic essentially Example Exercise extension fact finite follows formula Fredholm module function given gives graded Hence Hilbert space homology homomorphism homotopy ideal identity Index Theorem induces invariance inverse isometry isomorphism K-homology K-theory Kasparov Lemma linear manifold matrix metric modulo compact multiplication natural norm normal obtain projection proof Proposition Proposition Let prove reader relation relative Remark representation represented result Riemannian selfadjoint separable short exact sequence smooth space H spectrum subset supported Suppose Theorem theory Toeplitz topology unital unital C*-algebra unitarily equivalent unitary vector zero