Cubulation of Gromov-Thurston manifolds
type: Item
instance of: scholarly article
title: Cubulation of Gromov-Thurston manifolds
zbMATH Open document ID: 1376.57017
DOI: 10.4171/GGD/401
author: Anne Giralt
published in: Groups, Geometry, and Dynamics
publication date: 2017-08-10T00:00:00Z
review text: \textit{M. Gromov} and \textit{W. P. Thurston}, in their paper [Invent. Math. 89, 1--12 (1987; Zbl 0646.53037)], constructed an infinite family of Riemannian manifolds equipped with metrics of sectional curvature \(\leq -1\) and arbitrary close to 1, but which do not admit metrics of constant curvature. These manifolds are obtained as branched cyclic coverings over arithmetic manifolds. In the paper under review, the author proves that the fundamental groups of the Gromov-Thurston manifolds act geometrically on CAT(0) cube complexes. She also shows that these groups are linear over \(\mathbb{Z}\).
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 11F75
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 6759106
zbMATH Keywords: cube complex
zbMATH Keywords: branched cyclic covering
zbMATH Keywords: arithmetic manifold
zbMATH Keywords: hyperbolic manifold
zbMATH Keywords: Gromov-Thurston manifold
reviewed by: Athanase Papadopoulos
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/ggd/401
OpenAlex ID: W2656553296
description: scientific article; zbMATH DE number 6759106