Pseudo-Anosov homeomorphisms which extend to orientation reversing homeomorphisms of \(S^ 3\)
type: Item
instance of: scholarly article
title: Pseudo-Anosov homeomorphisms which extend to orientation reversing homeomorphisms of \(S^ 3\)
zbMATH Open document ID: 0653.57003
author: Tsuyoshi Kobayashi
published in: Osaka Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Infinitely many pseudo-Anosov homeomorphisms h of a closed surface \(F_ g\) of genus \(g>1\) are constructed which extend to the 3-sphere \(S^ 3\) exchanging the two complementary handle-bodies of the standard embedding of Fg in \(S^ 3\). As a consequence, identifying the boundaries of two copies of a handle-body of genus g by a power \(h^ n\) to obtain a Heegaard-splitting of a 3-manifold \(M_ n\), one obtains \(M_ n=S^ 3\), for n odd, and \(M_ n=\) the connected sum of g copies of \(S^ 2\times S^ 1\), for g even.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57R50
zbMATH DE Number: 4065937
zbMATH Keywords: pseudo-Anosov homeomorphisms of a closed surface
zbMATH Keywords: Heegaard-splitting
zbMATH Keywords: 3- manifold
reviewed by: Bruno Zimmermann
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4065937