Dan Burghelea: The homotopy type of the classifying space of the group of automorphisms of compact manifolds away of prime 2 and in "stability range”

ABSTRACT: I will review the description of the homotopy type of the classifying space of the group of automorphisms (diffeomorphisms / homeomorphisms) of a compact manifold M in "stability range" and "away of the prime 2" (known 40 years ago but apparently not well remembered today). I will also review the relations with the "moduli space of Riemannian structures" on M and with the space of "non parameterized closed curves" on M.