4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings
Metric Geometry
2019-12-19 v2 Differential Geometry
Group Theory
Abstract
We construct examples of smooth 4-dimensional manifolds M supporting a locally CAT(0)-metric, whose universal cover X satisfy Hruska's isolated flats condition, and contain 2-dimensional flats F with the property that the boundary at infinity of F defines a nontrivial knot in the boundary at infinity of X. As a consequence, we obtain that the fundamental group of M cannot be isomorphic to the fundamental group of any Riemannian manifold of nonpositive sectional curvature. In particular, M is a locally CAT(0)-manifold which does not support any Riemannian metric of nonpositive sectional curvature.
Cite
@article{arxiv.1002.4235,
title = {4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings},
author = {M. Davis and T. Januszkiewicz and J. -F. Lafont},
journal= {arXiv preprint arXiv:1002.4235},
year = {2019}
}
Comments
20 pages, 3 figures