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Dec 13 at 19:13 answer added Matthew Kvalheim timeline score: 0
Mar 4, 2021 at 1:20 comment added maxematician Even with a fine topology like $C^1$, or even $C^\infty$, can we find my desired conditions?
S Feb 13, 2021 at 4:02 history bounty ended CommunityBot
S Feb 13, 2021 at 4:02 history notice removed CommunityBot
Feb 5, 2021 at 3:39 comment added Tom Goodwillie Those topologies won't suffice. You need something like $C^1$.
Feb 5, 2021 at 3:13 comment added Kevin Casto If $\Phi$ and $\Phi'$ are homotopic, say $\phi(-,0) = \Phi$ and $\phi(-,1) = \Phi' $, then comparing level sets of $\Phi$ and $\Phi' $ just comes down to comparing level sets of $\phi$, in which case you need $\phi$ to have full rank on $\{c\} \times I$.
S Feb 5, 2021 at 2:55 history bounty started maxematician
S Feb 5, 2021 at 2:55 history notice added maxematician Draw attention
Nov 19, 2020 at 19:42 history asked maxematician CC BY-SA 4.0