Colloquium de Mathématiques :

Le 02 juin 2005 à 17:00 - Salle TD 32 - Batiment 9

Présentée par Singer Isadore M. - MIT

The Projective Dirac Operator and its Fractional Analytic Index.

I'll give an exposition of math.DG/0402329 [Mathai, Melrose, and Singer]. First I'll review the index theorem for the Dirac operator on spin manifolds coupled to vector bundles. Then I'll discuss a new index theorem when the manifold is not spin or spin_C for the Dirac "operator". It's index is now a rational number;I'll explain why. I'll indicate future directions at the end of my talk.