1
$\begingroup$

Let $f:X\to Y$ be a stratified map between Whitney stratified spaces such that for each stratum $S$ of $Y$, $f:f^{-1}(S)\to S$ is a proper stratified submersion. Let $\mathscr{T}_Y$ be a Thom-Mather control data of $Y$. Is there a Thom-Mather control data $\mathscr{T}_X$ on $X$ which is compatible with $\mathscr{T}_Y$ and $f$?

P.S. If Y has only one stratum, this is a theorem of Mather which is used to prove Thom's first isotropy lemma.

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.