Timeline for A modified version of the converse to the Sard's Theorem
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 1, 2022 at 23:01 | comment | added | Moishe Kohan | Reposted on MSE, here. | |
| May 27, 2022 at 23:33 | comment | added | pureorapplied | Hi Igor, thank you so much for your reference! However, I'm not familiar with the terminologies like smooth triangulation of manifolds...and I'm using the references in the paper to study it...Thus, is it possible to prove my claim above with only basic tools (like submersion) in differential topology? | |
| May 27, 2022 at 23:15 | comment | added | Igor Belegradek | Any open manifold admits a $C^1$ map to $\mathbb R$ without critical points, see Hirsch, Theorem 4.8 in [On Imbedding Differentiable Manifolds in Euclidean Space, Ann. Math, 1961], doi.org/10.2307/1970318. Composing the map with an inclusion of $\mathbb R$ into $\mathbb R^2$ gives a desired map with everywhere nonzero differential. | |
| May 27, 2022 at 21:35 | history | asked | pureorapplied | CC BY-SA 4.0 |