Hyperbolic manifolds of small volume
type: Item
instance of: scholarly article
title: Hyperbolic manifolds of small volume
zbMATH Open document ID: 1348.22013
author: Mikhail Belolipetsky
author: Vincent Emery
published in: Documenta Mathematica
publication date: 2014-10-21T00:00:00Z
full work available at URL: https://arxiv.org/abs/1310.2270
full work available at URL: 26.html
review text: Summary: We conjecture that for every dimension \(n \neq 3\) there exists a noncompact hyperbolic \(n\)-manifold whose volume is smaller than the volume of any compact hyperbolic \(n\)-manifold. For dimensions \(n \leq 4\) and \(n = 6\) this conjecture follows from the known results. In this paper we show that the conjecture is true for arithmetic hyperbolic \(n\)-manifolds of dimension \(n\geq 30\).
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 11E57
Mathematics Subject Classification ID: 20G30
Mathematics Subject Classification ID: 51M25
zbMATH DE Number: 6359320
zbMATH Keywords: hyperbolic manifold
zbMATH Keywords: volume
zbMATH Keywords: Euler characteristic
zbMATH Keywords: arithmetic group
MaRDI profile type: Publication
arXiv ID: 1310.2270
description: scientific article; zbMATH DE number 6359320