Curvature, diameter, and quotient manifolds

Burt Totaro

Curvature, diameter, and quotient manifolds

Differential Geometry 2007-05-23 v1 Algebraic Topology

Authors: Burt Totaro

Abstract

Gromov showed that there is an upper bound on the Betti numbers of all closed Riemannian n-manifolds of nonnegative sectional curvature. Grove asked whether such manifolds (if simply connected) fall into only finitely many rational homotopy types. We give a negative answer, in fact in dimension 6, which is the smallest possible. We also give counterexamples to some related questions in dimensions 7 and 9, improving the original counterexamples by Fang and Rong which were in dimensions at least 22.

Keywords

riemannian geometry ricci curvature and riemannian geometry manifolds

Cite

@article{arxiv.math/0209173,
  title  = {Curvature, diameter, and quotient manifolds},
  author = {Burt Totaro},
  journal= {arXiv preprint arXiv:math/0209173},
  year   = {2007}
}

Comments

12 pages

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