AN NCG APPROACH TO INDEX THEORY FOR MANIFOLDS WITH CORNERS

In this talk, I will review my joint work (published and on going) with Jean-Marie Lescure and Mario Velasquez, where we use groupoid and NCG techniques to study some problems in geometric analysis on manifolds with corners. In particular, I will review some K-theory computations (of the algebras of smoothing operators of the b-calculus of manifolds with corners) in terms of some very computable homology groups (conormal homology), and try to stress the important role of the use of some noncommutative spaces. I will also explain how these computations enter in the problem of finding geometric obstructions to some Fredholm boundary conditions. In the final part of the talk, I will review my work in progress with Jean-Marie in which we study the computation of several index morphisms (appearing in index theory for manifolds with corners) in terms of corner's conormal cycles.