4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings

Details 4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings 4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings

2010-02-23

arxiv.org/abs/1002.4235v2

Duke Math. Journal 161 (2012), pgs. 1-28

Mathematics

Metric Geometry

20 pages, 3 figures

Scientific paper

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.

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