Automorphism subgroups of finite index in algebraic mapping class groups
type: Item
instance of: scholarly article
title: Automorphism subgroups of finite index in algebraic mapping class groups
zbMATH Open document ID: 0873.20029
author: Warren Dicks
author: Edward Formanek
published in: Journal of Algebra
publication date: 1997-11-02T00:00:00Z
review text: The mapping class group of an orientable surface acts on the Teichmüller space giving rise to the corresponding moduli space. Many investigations into mapping class groups have thus utilised topological and analytic information in this analysis. For punctured surfaces, the fundamental groups are free and these mapping class groups may be described as outer automorphism groups of purely algebraically defined subgroups of the automorphism group of a free group. In this paper, the authors give purely algebraic analyses and proofs of results which relate the mapping class group of an \(n+1\)-punctured surface to that of the corresponding \(n\)-punctured surface. In particular, they analyse the nature of the automorphism (classes) in the kernel of the surjective map from the pure mapping class group \(PM_{g,n+1}\to PM_{g,n}\), first described using Dehn twists by \textit{J. S. Birman} [Commun. Pure Appl. Math. 22, 213-238 (1969; Zbl 0167.21503)]. Their analysis is linked to the work of \textit{J. McCool} [Publ. Mat., Barc. 40, No. 2, 457-468 (1996)].
Mathematics Subject Classification ID: 20F34
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 1013978
zbMATH Keywords: mapping class groups
zbMATH Keywords: punctured surfaces
zbMATH Keywords: fundamental groups
zbMATH Keywords: outer automorphism groups
reviewed by: C. Maclachlan
MaRDI profile type: Publication
full work available at URL: jabr.1996.6876
OpenAlex ID: W2014435761
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DOI: 10.1006/JABR.1996.6876
description: scientific article; zbMATH DE number 1013978