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Journal of the London Mathematical Society 2005 71(2):516-530; doi:10.1112/S002461070400612X
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© The London Mathematical Society

Stratified Transversality via Time-Dependent Vector Fields

C. Murolo, A. A. Du Plessis and D. J. A. Trotman

LATP (UMR 6632), Université de Provence 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France murolo{at}gyptis.univ-mrs.fr, trotman{at}gyptis.univ-mrs.fr
Matematisk Institut, Universitet Aarhus Ny Munkegade, 8000 Aarhus C, Denmark matadp{at}imf.au.dk

Received 3 August 2003.

For {chi} 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 : Z -> {chi} can be made transverse to a fixed stratified map g : y -> {chi}.


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