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C*-algebras and elliptic operators in differential topology

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Author(s): Solovyov Yu. P.; Troitsky E. V.
Series: Translations of mathematical monographs 192.
Publisher: American Mathematical Society
Year: 2001

Language: English
Pages: 213
City: Providence, R.I.

C*-Algebras and K-Theory --
Some facts from homological algebra --
C*-Hilbert modules --
K-Theory of C*-bundles --
Foundations of KK-theory --
Index Theorems --
Pseudodifferential operators --
The C*-index theorem --
The Atiyah-Singer theorem --
The Higher Signatures --
Characteristic classes --
Higher signatures of manifolds --
Hermitian K-theory and Fredholm representations --
Generalized Hirzebruch formulas --
Mishchenko's theorem --
Bruhat-Tits buildings and higher signatures --
Higher signatures and KK-theory --
Spinor manifolds, curvature and A-bundles --
Noncommutative Differential Geometry --
Cyclic and dihedral homology --
Chern character, index, and Lefschetz numbers --
The Connes-Moscovici theorem.