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STRATIFIED TRANSVERSALITY VIA TIME-DEPENDENT VECTOR FIELDS

Published online by Cambridge University Press:  06 April 2005

C. MUROLO ,
A. A. DU PLESSIS  and
D. J. A. TROTMAN
C. MUROLO
Affiliation:
LATP (UMR 6632), Université de Provence, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, [email protected], [email protected]
A. A. DU PLESSIS
Affiliation:
Matematisk Institut, Universitet Aarhus, Ny Munkegade, 8000 Aarhus C, [email protected]
D. J. A. TROTMAN
Affiliation:
LATP (UMR 6632), Université de Provence, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, [email protected], [email protected]
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Abstract

For ${\cal X}$ a stratification with suitable regularity, in particular for any Whitney stratification and, via regular embedding, for any abstract stratified set, time-dependent vector fields are used to prove an extension theorem for diffeomorphisms near the identity defined on strata of a given dimension. Then it is shown that after isotopy a stratified map $h\,{:}\,{\cal Z} \,{\longrightarrow}\, {\cal X}$ can be made transverse to a fixed stratified map $g\,{:}\, {\cal Y} \,{\longrightarrow}\, {\cal X}$.

Keywords

58A3557N75 (primary)54C2057R52 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 516 - 530
Copyright
The London Mathematical Society 2005

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