Classes d'isotopie de plongements de 1-complexes dans les surfaces
type: Item
instance of: scholarly article
title: Classes d'isotopie de plongements de 1-complexes dans les surfaces
zbMATH Open document ID: 0584.57006
DOI: 10.1016/0040-9383(84)90013-2
author: Yves Ladegaillerie
published in: Topology
publication date: 1984-01-01T00:00:00Z
review text: As generalization of the Baer theorem the following theorem is proved: Let the compact orientable surface X with boundary be obtained as the union of two orientable surfaces T and \(\Sigma\) having in common part of their boundaries. Then there is a finite family F of curves in T with the following property: if h is any orientation preserving homeomorphism of X which maps every curve \(\gamma\) of F into a curve homotopic to \(\gamma\) in X then h is isotopic in X to a homeomorphism h' of X which is the identity on T. The proof does not use the known Baer theorem on isotopies. The theorem has interesting applications: 1) Let \(i_ 0\) and \(i_ 1\) be embeddings of a 1-complex K into the interior of an orientable compact surface X with boundary. Then \(i_ 0\) and \(i_ 1\) are ambient isotopic iff they are homotopic and there is a homeomorphism h of X with \(h\circ i_ 0=i_ 1\). 2) A similar result for embeddings of one surface X into another X'.
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57R40
zbMATH DE Number: 3935987
zbMATH Keywords: embeddings of surface
zbMATH Keywords: compact orientable surface with boundary
zbMATH Keywords: orientation preserving homeomorphism
zbMATH Keywords: isotopic
zbMATH Keywords: Baer theorem on isotopies
MaRDI profile type: Publication
full work available at URL: 0040-9383(84)90013-2
OpenAlex ID: W2067217014
description: scientific article; zbMATH DE number 3935987