Extension problem of diffeomorphisms of a 3-torus over some 4-manifolds
type: Item
instance of: scholarly article
title: Extension problem of diffeomorphisms of a 3-torus over some 4-manifolds
zbMATH Open document ID: 0548.57005
author: Takao Matumoto
published in: Hiroshima Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: A K3 surface is a union of two copies of a half K3 surface N. It is proved that the diffeomorphism type of \(N\cup N\) does not depend on the choice of attaching orientation reversing diffeomorphism of the boundary 3-torus. A Poincaré homology 3-sphere H(1,1,1) is cobordant to a 3- torus \(T^ 3\) by a cobordism W(1,1,1) given by attaching three 2 handles to \(T^ 3\times [0,1]\) at three standard generators on \(T^ 3\) with framing numbers 1, 1 and 1. The paper actually proves that any orientation preserving diffeomorphism f of \(T^ 3\) extends to a diffeomorphism F of the cobordism W(1,1,1) so that \(F| H(1,1,1)=id\). Since \(N\supset W(1,1,1)\) so that \(\partial W(1,1,1)\supset\partial N\), the first statement follows directly. A similar result for W(0,0,0) is also proved.
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57R65
zbMATH DE Number: 3874228
zbMATH Keywords: 4-dimensional manifold
zbMATH Keywords: extending diffeomorphism from a boundary component to a cobordism
zbMATH Keywords: attaching 2 handles
zbMATH Keywords: K3 surface
zbMATH Keywords: diffeomorphism type
zbMATH Keywords: Poincaré homology 3-sphere
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3874228