Hyperbolization and regular neighborhoods

2020/11/02 by Belegradek, Igor
#57N55 #57Q40 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Primary 53C23 #Secondary 20F67

paper · doi:10.48550/arxiv.2011.01320

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.

Related

• Riemannian Hyperbolization
• Topological regular neighborhoods
• Closed, negatively curved Riemannian manifolds with a flat horosphere are hyperbolic
• Nonpositively curved manifolds containing a prescribed nonpositively curved hypersurface
• On strictly convex subsets in negatively curved manifolds