Classes d'isotopie de plongements de 1-complexes dans les surfaces
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'.
compact orientable surface with boundary
scientific article; zbMATH DE number 3935987