Hyperbolic 3-manifolds with totally geodesic boundary
type: Item
instance of: scholarly article
title: Hyperbolic 3-manifolds with totally geodesic boundary
zbMATH Open document ID: 0727.57010
author: Michihiko Fujii
published in: Osaka Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: For an integer \(g\geq 2\) let \(M_ g\) be the Riemann moduli space of isometry classes of closed hyperbolic surfaces of genus g. A claim by Thurston is that the subset S of \(M_ g\) consisting of those surfaces which bound compact hyperbolic 3-manifolds (with totally geodesic boundaries) is a countably infinite dense subset of \(M_ g\). The author constructs for each fixed \(g\geq 2\) infinitely many non-isometric compact oriented hyperbolic 3-manifolds with totally geodesic boundary of genus g. He conjectures that the boundary surfaces in these examples have different moduli.
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 4201159
zbMATH Keywords: moduli space
zbMATH Keywords: hyperbolic surfaces
zbMATH Keywords: genus
zbMATH Keywords: hyperbolic 3-manifolds
reviewed by: Wolfgang Heil
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4201159