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Topology of ends of nonpositively curved manifolds

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NPCW05 - Group actions and cohomology in non-positive curvature

Co-author: Tam Nguyen Phan (Binghamton University)

The structure of ends of a finite volume, nonpositively curved, locally symmetric manifold M is very well understood. By Borel-Serre, the thin part of the universal cover of such a manifold is homotopy equivalent to a rational Tits building. This is a simplicial complex built out of the algebra of the locally symmetric space which turns out to have dimension = dim M/2. Another application is that the group cohomology with group ring coefficients of the fundamental group of M vanishes in low dimensions (

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