Bott-Samelson varieties factor the flag variety G/B into a product of CP’s with a map into G/B. These varieties are mostly studied in the case in which the map into G/B is birational; however in this paper we study fibers of this map when it is not birational. We will see that in some cases this fiber is a toric variety. In order to do so we use the moment map of a Bott-Samelson variety to tran...

We give a topological interpretation of the space of L-harmonic forms of finite-volume manifolds with sufficiently pinched negative curvature. We give examples showing that this interpretation fails if the curvature is not sufficiently pinched. The method used applies to other situations, e.g. asymptotically complex hyperbolic manifolds, or harmonic forms with weights. Résumé Nous donnons une i...

We give a topological interpretation of the space of L-harmonic forms of finite-volume manifolds with sufficiently pinched negative curvature. We give examples showing that this interpretation fails if the curvature is not sufficiently pinched and that our result is sharp with respect to the pinching constants. The method consists first in comparing L2−cohomology with weighted L2−cohomology tha...

L’objet de cette Note est d’établir une réalisation géométrique l’isomorphisme cohomologique dans le cas d’un feuilletage Killing transversalement orienté sur variété compacte à travers les caractères Chern basiques équivariants.