Cohomologie $L^2$ et parabolicite
  We obtain a topological interpretation for the space of $L^2$ harmonic forms for some complete Riemannian manifold : when the geometry at infinity is the geometry of a simply connected nilpotent Lie group, when the geometry at infinity is a symmetric space with non positive curvature and also when the geometry at infinity is parabolic. 
Gilles Carron (LMJL)