Difféomorphismes commutants des surfaces et stabilité des fibrations en tores. (Commuting diffeomorphisms of surfaces and stability of fibrations by tori)
type: Item
instance of: scholarly article
title: Difféomorphismes commutants des surfaces et stabilité des fibrations en tores. (Commuting diffeomorphisms of surfaces and stability of fibrations by tori)
zbMATH Open document ID: 0703.57015
DOI: 10.1016/0040-9383(90)90027-H
published in: Topology
publication date: 1990-01-01T00:00:00Z
review text: The paper contains two partial solutions of Rosenberg's problem concerning the stability of fibres of a fibre bundle by tori over a surface. These are the following: 1) Let S be a compact surface with the non-vanishing Euler characteristic. For each \(n\in {\mathbb{N}}\), there exists a neighbourhood \(\mu_ n\) of the identity in \(Diff_ 1(S)\) such that if \(f_ 1,...,f_ n\in \mu_ n\) are diffeomorphisms of S such that \(f_ if_ j=f_ jf_ i\) for \(i,j=1,...,n\), then they have a common fixed point. 2) Let S be an oriented surface of genus \(g>1\). There exists a fibre bundle over S with fibre \(T_ 2\) and a family \(\{\) \({\mathcal F}_ t\}_{t\in {\mathbb{R}}}\) of foliations depending smoothly on t, such that \({\mathcal F}_ 0\) is defined by a fibre bundle and, for each \(t\neq 0\), \({\mathcal F}_ t\) has no compact leaf.
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 57R50
zbMATH DE Number: 4153490
zbMATH Keywords: commuting diffeomorphisms of a surface
zbMATH Keywords: foliation defined by a fibre bundle
zbMATH Keywords: stability of compact leaves
zbMATH Keywords: fibre bundle over an oriented surface with fibre \(T^ 2\)
zbMATH Keywords: common fixed point
author: C. Bonatti
MaRDI profile type: Publication
Wikidata QID: Q127211990
description: scientific article; zbMATH DE number 4153490