The index theorem for almost periodic operators and foliations
We first explain how operator algebras can be used to get an index theorem for uniformly elliptic almost periodic operators. Then, we explain what is the index theorem for foliations, and how it has been solved by A. Connes.
Locality and the Dixmier's trace
The Dixmier's trace was introduced in the proof of the local index theorem for spectral triples. We give a general definition of the Dixmier's trace in the context of semi-finite von Neumann algebras, and relate it to the Wodzicki residue in the above examples.
The index theorem for von Neumann spectral triples
We explain what is the Connes-Moscovici local index theorem for von Neumann spectral triples.
Updated 04/03/2005