Counting open negatively curved manifolds up to tangential homotopy equivalence
Differential Geometry
2007-05-23 v1 Group Theory
Geometric Topology
Metric Geometry
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.
Keywords
Cite
@article{arxiv.math/9809014,
title = {Counting open negatively curved manifolds up to tangential homotopy equivalence},
author = {Igor Belegradek},
journal= {arXiv preprint arXiv:math/9809014},
year = {2007}
}
Comments
22 pages, no figures; to appear in Journal of Differential Geometry