Counting open negatively curved manifolds up to tangential homotopy equivalence

Igor Belegradek

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Counting open negatively curved manifolds up to tangential homotopy equivalence

Igor Belegradek

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Abstract

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.

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BibTeX RIS

Igor Belegradek. 1998-09-03. Counting open negatively curved manifolds up to tangential homotopy equivalence. https://arxiv.org/abs/math/9809014

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