Sur la L2-cohomologie des varietes a courbure negative

Details Sur la L2-cohomologie des varietes a courbure negative Sur la L2-cohomologie des varietes a courbure negative

2002-07-12

arxiv.org/abs/math/0207111v3

Mathematics

Differential Geometry

New version. We improve our main result, which is now optimal

Scientific paper

We give a topological interpretation of the space of L2-harmonic forms on 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 thanks to previuos works done by T. Ohsawa, and then in identifying these weighted spaces.

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