Cohomologie $L^2$ et parabolicité

Gilles Carron (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: $L^2$ cohomology; parabolicity

Domaines: Géométrie différentielle [math.DG]

Gilles Carron. Cohomologie $L^2$ et parabolicité. Journal of Geometric Analysis, 2005, 15, pp.391--404. ⟨hal-00002191v2⟩