Hyperbolization and regular neighborhoods
Differential Geometry
2020-11-04 v1 Group Theory
Geometric Topology
Abstract
We show that the hyperbolization of polyhedra pulls back regular neighborhoods of PL submanifolds. Applying this to the Riemannian version of the hyperbolization due to Ontaneda gives open complete manifolds of pinched negative curvature that are homotopy equivalent to closed smooth manifolds but contain no smooth spines. We also find open complete negatively pinched manifolds that are homotopy equivalent to closed non-smoothable manifolds.
Keywords
Cite
@article{arxiv.2011.01320,
title = {Hyperbolization and regular neighborhoods},
author = {Igor Belegradek},
journal= {arXiv preprint arXiv:2011.01320},
year = {2020}
}
Comments
27 pages