Counting open negatively curved manifolds up to tangential homotopy equivalence

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Under mild assumptions on a group G, we prove that the class of complete Riemannian n-manifolds of uniformly bounded negative sectional curvatures and with the fundamental groups isomorphic to G breaks into finitely many tangential homotopy types. It follows that many aspherical manifolds do not admit complete negatively curved metrics with prescribed curvature bounds.
22 pages, no figures; to appear in Journal of Differential Geometry

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Differential Geometry, Group Theory, Geometric Topology, Metric Geometry, 53C23; 20F32; 55R50; 57S30

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http://salesiana.dossiersoluciones.com/handle/123456789/77348

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9809014
 http://arxiv.org/abs/math/9809014

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arXiv