Interiors of compact contractible \(n\)-manifolds are hyperbolic \((n\geq 5)\)
type: Item
instance of: scholarly article
title: Interiors of compact contractible \(n\)-manifolds are hyperbolic \((n\geq 5)\)
zbMATH Open document ID: 0877.53030
author: Fredric D. Ancel
author: Craig R. Guilbault
published in: Journal of Differential Geometry
publication date: 1997-12-02T00:00:00Z
review text: The interior of every compact contractible PL \(n\)-manifold \((n\geq 5)\) supports a complete geodesic metric of strictly negative curvature. This provides a new family of simple examples illustrating the negative answer to a question of M. Gromov which asks whether metrically convex geodesic spaces which are topological manifolds must be homeomorphic to Euclidean spaces. The first examples verifying the negative answer to this question were given by \textit{M. W. Davis} and \textit{T. Januszkiewicz} [J. Differ. Geom. 34, 347-386 (1991; Zbl 0723.57017)].
Mathematics Subject Classification ID: 53C23
zbMATH DE Number: 1026530
zbMATH Keywords: PL-manifold
zbMATH Keywords: non-positive curvature
zbMATH Keywords: Cartan-Hadamard theorem
zbMATH Keywords: CAT(0) spaces
zbMATH Keywords: negative curvature
zbMATH Keywords: metrically convex geodesic spaces
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214459752
OpenAlex ID: W1597938318
Wikidata QID: Q115175996
DOI: 10.4310/JDG/1214459752
description: scientific article; zbMATH DE number 1026530