دانلود کتاب Basic noncommutative geometry

فهرست مطالب :

Contents......Page 8
Introduction......Page 10
Locally compact spaces and commutative C*-algebras......Page 18
Vector bundles, finite projective modules, and idempotents......Page 32
Affine varieties and finitely generated commutative reduced algebras......Page 38
Affine schemes and commutative rings......Page 41
Compact Riemann surfaces and algebraic function fields......Page 42
Sets and Boolean algebras......Page 43
From groups to Hopf algebras and quantum groups......Page 44
Groupoids......Page 60
Groupoid algebras......Page 65
Morita equivalence......Page 77
Morita equivalence for C*-algebras......Page 86
Noncommutative quotients......Page 92
Sources of noncommutative spaces......Page 99
Cyclic cohomology......Page 100
Hochschild cohomology......Page 102
Hochschild cohomology as a derived functor......Page 108
Deformation theory......Page 115
Topological algebras......Page 125
Examples: Hochschild (co)homology......Page 128
Cyclic cohomology......Page 137
Connes\' long exact sequence......Page 149
Connes\' spectral sequence......Page 153
Cyclic modules......Page 156
Examples: cyclic cohomology......Page 161
Connes–Chern character in K-theory......Page 167
Connes–Chern character in K-homology......Page 180
Algebras stable under holomorphic functional calculus......Page 197
A final word: basic noncommutative geometry in a nutshell......Page 201
A.1 Gelfand’s theory of commutative Banach algebras......Page 203
A.2 States and the GNS construction......Page 207
B Compact operators, Fredholm operators, and abstract index theory......Page 214
C Projective modules......Page 221
D Equivalence of categories......Page 223
Bibliography......Page 226
Index......Page 236