Isometric cusps in hyperbolic \(3\)-manifolds
type: Item
instance of: scholarly article
title: Isometric cusps in hyperbolic \(3\)-manifolds
zbMATH Open document ID: 0961.57010
author: Colin Adams
published in: Michigan Mathematical Journal
publication date: 2001-01-01T00:00:00Z
review text: Two cusps in a cusped finite volume hyperbolic \(3\)-manifold are called maximally isometric if their corresponding maximal cusps have isometric interiors. This paper provides a list of cusps, defined up to maximal isometry, such that given any cusp from the list and any cusped finite volume hyperbolic \(3\)-manifold \(M\), there exist two disjoint simple closed curves in \(M\) with the property that if we put a finite volume hyperbolic metric on the complement of the curves in \(M\), then one of the new cusps is maximally isometric to \(C\). Since any closed \(3\)-manifold becomes finite volume hyperbolic after removing a simple closed curve, the same result holds if \(M\) is any closed \(3\)-manifold and three disjoint simple closed curves are removed.
reviewed by: Igor Belegradek
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 1548330
zbMATH Keywords: cusp
zbMATH Keywords: link
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1030132477
OpenAlex ID: W2078754597
DOI: 10.1307/MMJ/1030132477
description: scientific article; zbMATH DE number 1548330