Counting open negatively curved manifolds up to tangential homotopy equivalence

Details Counting open negatively curved manifolds up to tangential homotopy equivalence Counting open negatively curved manifolds up to tangential homotopy equivalence

1998-09-03

arxiv.org/abs/math/9809014v1

Mathematics

Differential Geometry

22 pages, no figures; to appear in Journal of Differential Geometry

Scientific paper

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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