Jean-Marie Lescure, Université Blaise Pascal de Clermont-Ferrand:
Groupoids and index theory for singular spaces.
We will see how the non commutative tangent space of manifold
with conical singularities can be used to produce analytical and
topological
index maps similar to those defined by M. Atiyah and I. Singer on a
smooth
manifold. In the conical case, we will briefly explain how the
analytical
index map is related to Fredholm index of suitable elliptic operators.
We will show how the framework of groupoids unify the smooth and
conical
cases.
Then, we will present partial advances in the generalization of the
previous
ideas for general stratified spaces.