Analytic K-HomologyAnalytic 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. |
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תוכן
LXIX | 188 |
LXX | 196 |
LXXI | 198 |
LXXII | 199 |
LXXIV | 204 |
LXXV | 208 |
LXXVI | 212 |
LXXVII | 215 |
X | 22 |
XI | 27 |
XII | 29 |
XIV | 32 |
XV | 34 |
XVI | 36 |
XVII | 38 |
XVIII | 40 |
XIX | 41 |
XX | 44 |
XXI | 49 |
XXII | 54 |
XXIII | 55 |
XXV | 57 |
XXVI | 60 |
XXVII | 63 |
XXVIII | 65 |
XXIX | 68 |
XXX | 71 |
XXXI | 76 |
XXXII | 79 |
XXXIII | 83 |
XXXIV | 85 |
XXXVI | 90 |
XXXVII | 92 |
XXXVIII | 97 |
XXXIX | 98 |
XL | 101 |
XLI | 103 |
XLII | 106 |
XLIII | 110 |
XLIV | 113 |
XLV | 120 |
XLVI | 123 |
XLVIII | 125 |
XLIX | 130 |
L | 133 |
LI | 137 |
LII | 138 |
LIII | 139 |
LIV | 141 |
LVI | 145 |
LVII | 147 |
LVIII | 152 |
LIX | 157 |
LX | 160 |
LXI | 162 |
LXII | 165 |
LXIII | 167 |
LXIV | 168 |
LXV | 170 |
LXVI | 180 |
LXVII | 183 |
LXVIII | 186 |
LXXVIII | 219 |
LXXIX | 223 |
LXXX | 233 |
LXXXI | 237 |
LXXXII | 239 |
LXXXIV | 243 |
LXXXV | 248 |
LXXXVI | 252 |
LXXXVII | 253 |
LXXXVIII | 259 |
LXXXIX | 264 |
XC | 265 |
XCI | 267 |
XCII | 269 |
XCIII | 271 |
XCIV | 274 |
XCV | 279 |
XCVI | 284 |
XCVII | 286 |
XCVIII | 290 |
XCIX | 293 |
C | 297 |
CI | 303 |
CII | 305 |
CIII | 306 |
CIV | 311 |
CV | 318 |
CVI | 320 |
CVII | 326 |
CVIII | 329 |
CIX | 333 |
CX | 341 |
CXI | 345 |
CXII | 347 |
CXIV | 350 |
CXV | 352 |
CXVI | 357 |
CXVII | 363 |
CXVIII | 369 |
CXIX | 373 |
CXX | 375 |
CXXI | 377 |
CXXIII | 378 |
CXXIV | 379 |
CXXV | 380 |
CXXVI | 384 |
CXXVII | 385 |
CXXVIII | 387 |
CXXIX | 388 |
CXXX | 389 |
CXXXI | 390 |
391 | |
401 | |
מהדורות אחרות - הצג הכל
מונחים וביטויים נפוצים
abelian group ample representation associated Bott Periodicity boundary map bounded operator C*-algebra Chapter Co(X commutes modulo compacts compact operators compactly supported completely positive map construction continuous functions defined Definition Let denote diagram differential operator Dirac bundle Dirac operator direct sum domain element elliptic operator essential spectrum essentially selfadjoint Example Exercise finite finite-dimensional follows formula Fredholm module Fredholm operator functor Hermitian Hilbert space homology homomorphism homotopy invariance index pairing Index Theorem induces an isomorphism inverse isometry isomorphism K-homology K-homology class K-homology groups K-theory K-theory groups Kasparov product Ko(A KP(A Lemma Let linear locally compact matrix modulo compact operators multigraded multiplication norm obtain operator on H orthogonal p-multigraded projection Proposition Let prove Remark Riemannian manifold Schrodinger pair selfadjoint selfadjoint operator separable C*-algebras short exact sequence smooth space H Spinc-structure spinor bundle subspace Suppose tensor product theory topology unital C*-algebra unitarily equivalent unitary vector bundle zero