Surfaces in 4-manifolds and their mapping class groups
type: Item
instance of: scholarly article
title: Surfaces in 4-manifolds and their mapping class groups
zbMATH Open document ID: 1197.57019
author: Susumu Hirose
author: Akira Yasuhara
published in: Topology
publication date: 2009-04-16T00:00:00Z
review text: There are deformations of embedded surfaces in 4-manifolds which induce isotopically non-trivial diffeomorphisms on surfaces. These deformations define extensions of isotopically non-trivial diffeomorphisms on surfaces. It is known that any orientation preserving diffeomorphism of a surface embedded in the complex projective plane is extendable. In the present paper, the authors investigate embedded surfaces in some other smooth 4-manifolds, for which the same kind of phenomena happen. A surface in a smooth 4-manifold is called flexible if, for any diffeomorphism \(\phi\) on the surface, there is a diffeomorphism on the 4-manifold whose restriction to the surface is \(\phi\) and which is isotopic to the identity. The authors investigate a sufficient condition for a smooth 4-manifold \(M\) to include flexible knotted surfaces. They also introduce a local operation in simply connected 4-manifolds for obtaining a flexible knotted surface from any knotted surface.
Mathematics Subject Classification ID: 57M99
zbMATH DE Number: 5544217
zbMATH Keywords: 4-dimensional manifold
zbMATH Keywords: mapping class group
zbMATH Keywords: knotted surface
reviewed by: Maciej Niebrzydowski
MaRDI profile type: Publication
full work available at URL: j.top.2007.05.001
OpenAlex ID: W2064316996
DOI: 10.1016/J.TOP.2007.05.001
description: scientific article; zbMATH DE number 5544217