Geometry of cubulated 3-manifolds
type: Item
instance of: scholarly article
title: Geometry of cubulated 3-manifolds
zbMATH Open document ID: 0869.57015
DOI: 10.1016/0040-9383(94)00050-6
author: Lee Mosher
published in: Topology
publication date: 1996-04-08T00:00:00Z
review text: A part of the geometrization conjecture for 3-manifolds reduces to the hyperbolization conjecture that a closed, orientable irreducible 3-manifold \(M\) with infinite fundamental group either is hyperbolic or has a \(\mathbb{Z}^2\) subgroup contained in \(\tau_1(M)\). This paper establishs a weakened form of the hyperbolization conjecture for cubulated 3-manifolds of nonpositive curvature: If \(M\) is a connected, cubulated 3-manifold of nonpositive curvature, then either \(M\) is negatively curved in the sense of Gromov, or \(\pi_1(M)\) has a \(\mathbb{Z}^2\) subgroup. (Note that a cubulation is like a triangulation using cubes and squares instead of tetrahedra and triangles).
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 863706
zbMATH Keywords: geometrization conjecture
zbMATH Keywords: 3-manifolds
zbMATH Keywords: hyperbolization conjecture
zbMATH Keywords: cubulated 3-manifolds
reviewed by: James Hebda
MaRDI profile type: Publication
full work available at URL: 0040-9383(94)00050-6
OpenAlex ID: W2008998040
description: scientific article; zbMATH DE number 863706