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arXiv · 1212.3303

Non-aspherical ends and nonpositive curvature

Igor Belegradek·T. Tam Nguyen Phan
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Abstract

We obtain restrictions on the topology of a closed connected manifold B that bounds a (possibly noncompact) manifold whose interior V admits a complete Riemannian metric of nonpositive sectional curvature. If G denotes the fundamental group of B, then a sample result is that B must be aspherical and incompressible if one of the following is true: (1) V has finite volume and G is virtually nilpotent, (2) G is virtually nilpotent and has no proper torsion-free quotients, (3) G is isomorphic to a uniform, irreducible lattice of real rank > 1.

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Igor Belegradek, T. Tam Nguyen Phan. 2014-08-03. Non-aspherical ends and nonpositive curvature. https://arxiv.org/abs/1212.3303

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