Stratified transversality time-dependent vector fields. (English) Zbl 1108.58003
A diffeomorphism extension theorem is established for certain stratified spaces, including Whitney stratified spaces. The diffeomorphism that is extended is assumed close to the identity and defined on strata of a given dimension. The proof uses time-dependent vector fields. It is also shown that a stratified map is isotopic to a map that is transverse to another fixed stratified map.
Reviewer: Bruce Hughes (Nashville)
MSC:
58A35 | Stratified sets |
57N75 | General position and transversality |
54C20 | Extension of maps |
57R52 | Isotopy in differential topology |
57N80 | Stratifications in topological manifolds |