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Diffeomorphisms lying in one-parameter groups and extension of stratified homeomorphisms

Published online by Cambridge University Press:  26 March 2001

CLAUDIO MUROLO
CLAUDIO MUROLO
Affiliation:
Université de Provence, Centre de Mathématiques et Informatique 39, rue Joliot-Curie, 13453 Marseille Cedex 13, France; e-mail: [email protected]
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Abstract

In this note we first show, using results of McDuff, that for a Cr-manifold S, diffeomorphic to the interior of a compact manifold with boundary, the class of all Cr-diffeomorphisms lying in a one parameter group of S generates the connected component of 1S in Diffr (S, S). Then we use this result to obtain two extension theorems for stratified maps defined on some strata of a stratified space [Xscr ]. Our extension theorems hold for Mather's abstract stratified sets, for Whitney (b)-regular, Bekka (c)-regular, Verdier (w)-regular and Lipschitz-regular stratified spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 2 , March 2001 , pp. 333 - 341
Copyright
2001 Cambridge Philosophical Society

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