The structure of subgroup of mapping class groups generated by two Dehn twists
type: Item
instance of: scholarly article
title: The structure of subgroup of mapping class groups generated by two Dehn twists
zbMATH Open document ID: 0883.57016
author: Atsushi Ishida
published in: Proceedings of the Japan Academy. Series A
publication date: 1997-07-23T00:00:00Z
review text: If \(a\) and \(b\) are simple closed curves on an \(n\)-punctured orientable surface of genus \(g\) then the Dehn twists \(\tau_a\), \(\tau_b\) along \(a\) and \(b\), respectively, generate a subgroup \(H\) of the mapping class group \({\mathcal M}_{g,n}\). The author shows that \(H\) is free if the minimal intersection number of \(a\) and \(b\) is at least 2.
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57S05
zbMATH DE Number: 1022280
zbMATH Keywords: mapping class group
reviewed by: Wolfgang Heil
MaRDI profile type: Publication
full work available at URL: pjaa.72.240
OpenAlex ID: W2042679941
cites work: Braids, Links, and Mapping Class Groups. (AM-82)
cites work: Q4040246
cites work: Q3891436
DOI: 10.3792/PJAA.72.240
description: scientific article; zbMATH DE number 1022280