Next:
Contents
Contents
Foliations, C*-algebras and index theory
Part I, II
Henri Moscovici
notes taken by:
Contents
Introduction
Foliations
What is a foliation and why is it interesting ?
Equivalent definitions
Holonomy grupoid
How to handle ``
''
Characteristic classes
Characteristic classes
Preamble: Chern-Weil construction of Pontryagin ring
Adapted connection and Bott's theorem
The Godbillon-Vey class
Nontriviality of Godbillon-Vey class
Naturality under transversality
Transgressed classes
Weil algebras
The truncated Weil algebras and characteristic homomorphism
and framed foliations
Gelfand-Fuks cohomology
Cohomology of Lie algebras
Gelfand-Fuks cohomology
Some "soft" results
Spectral sequences
Exact couples
Filtered complexes
Illustration of convergence
Hochschild-Serre spectral sequence
Characteristic maps and Gelfand-Fuks cohomology
Jet groups
Jet bundles
Characteristic map for foliation
Index theory and noncommutative geometry
Classical index theorems
General formulation and proto-index formula
Multilinear reformulation: cyclic cohomology (Connes)
Connes cyclic cohomology
An alternate route, via the Families Index Theorem
Index theory for foliations
Hopf cyclic cohomology
Preliminaries
Cyclic cohomology in abelian category
Hopf algebras
Motivation for Hopf-cyclic cohomology
Hopf-cyclic cohomology with coefficients
Special cases
The Hopf algebra
About this document ...
Pawel Witkowski 2006-03-14
''
and framed foliations