Convergence groups and Seifert fibered 3-manifolds
type: Item
instance of: scholarly article
title: Convergence groups and Seifert fibered 3-manifolds
zbMATH Open document ID: 0840.57005
DOI: 10.1007/BF01231540
published in: Inventiones Mathematicae
publication date: 1996-07-01T00:00:00Z
full work available at URL: https://eudml.org/doc/144243
review text: The authors give a new proof of D. Gabai's result, that if \(S^1\) has a fixed orientation and \(T\) denotes the set of ordered triples \((x,y,z)\) of distinct points occurring in positive order on \(S^1\), acted on by \(\text{Homeo}_+ (S^1)\) in the obvious way, and if \(\Gamma \subset \text{Homeo}_+ (S^1)\) is a discrete convergence group, then \(T/ \Gamma\) is Seifert fibred. (By work of G. Mess and P. Scott, this implies the Seifert Fibre Space Conjecture.) The proof is by means of braid theory.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M60
zbMATH DE Number: 703863
zbMATH Keywords: Seifert fibred
zbMATH Keywords: braid
zbMATH Keywords: convergence group
author: Andrew J. Casson
author: Douglas S. Jungreis
reviewed by: C. Kearton
MaRDI profile type: Publication
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OpenAlex ID: W2091639308
description: scientific article; zbMATH DE number 703863