Involutions in surface mapping class groups
type: Item
instance of: scholarly article
title: Involutions in surface mapping class groups
zbMATH Open document ID: 0655.57005
author: Athanase Papadopoulos
author: John D. McCarthy
published in: L'Enseignement Mathématique. 2e Série
publication date: 1987-01-01T00:00:00Z
review text: As first result it is proved that the mapping class group M(F) of a closed orientable surface F of genus \(g>2\) is generated by involutions (elements of order 2). Then the possible types of the product of two involutions in M(F) are analysed, by considering the action of M(F) on the Thurston-compactification K of the Teichmüller space \(T\subset K\) of F. According to the relative position of the fixed point sets of the 2 involutions, such a product will be of finite order (common fixed point in T), reducible (common fixed point in K but not in T) or pseudo-Anosov (no common fixed point), in strong analogy to the possible types of the product of two elliptic involutions on the Poincaré-disc (elliptic, parabolic or hyperbolic).
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57R50
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 20F34
zbMATH DE Number: 4069834
zbMATH Keywords: Thurston-compactification of the Teichmüller space
zbMATH Keywords: mapping class group of a closed orientable surface
zbMATH Keywords: involutions
zbMATH Keywords: product of two involutions
zbMATH Keywords: reducible
zbMATH Keywords: pseudo-Anosov
zbMATH Keywords: product of two elliptic involutions
reviewed by: Bruno Zimmermann
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4069834