Duke Mathematical Journal
- Duke Math. J.
- Volume 161, Number 1 (2012), 1-28.
4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings
We construct examples of 4-dimensional manifolds supporting a locally CAT(0)-metric, whose universal covers satisfy Hruska’s isolated flats condition, and contain -dimensional flats with the property that are nontrivial knots. As a consequence, we obtain that the group cannot be isomorphic to the fundamental group of any compact Riemannian manifold of nonpositive sectional curvature. In particular, if is any compact locally CAT(0)-manifold, then is a locally CAT(0)-manifold which does not support any Riemannian metric of nonpositive sectional curvature.
Duke Math. J., Volume 161, Number 1 (2012), 1-28.
First available in Project Euclid: 30 December 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Davis, M.; Januszkiewicz, T.; Lafont, J.-F. 4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings. Duke Math. J. 161 (2012), no. 1, 1--28. doi:10.1215/00127094-1507259. https://projecteuclid.org/euclid.dmj/1325264704