$L^2$ cohomology of Manifolds with flat ends

Details $L^2$ cohomology of Manifolds with flat ends $L^2$ cohomology of Manifolds with flat ends

2001-11-07

arxiv.org/abs/math/0111070v1

Mathematics

Differential Geometry

29 pages

Scientific paper

We give a topological interpretation of the space of $L^2$-harmonic forms on Manifold with flat ends. It is an answer to an old question of J. Dodziuk. We also give a Chern-Gauss-Bonnet formula for the $L^2$-Euler characteristic of some of these Manifolds. These results are applications of general theorems on complete Riemannian Manifold whose Gauss-Bonnet operator is non-parabolic at infinity.

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