L² cohomology of Manifolds with flat ends

2001/11/07 by Gilles Carron, Carron, Gilles · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.AP #math.DG #msc:35J25 #msc:53C21 #msc:58C40 #msc:58J10

paper · pdf · doi:10.48550/arxiv.math/0111070

29 pages

arxiv created 2001/11/07 · arxiv updated 2009/11/30

Abstract

We give a topological interpretation of the space of L²-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 L²-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.

Cited by

• On the Interplay Between Hodge Projections and Bounded Harmonic Functions on Manifolds with Ends

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