Timeline for On "graphs" of foliations
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| S Nov 2, 2022 at 23:08 | history | bounty ended | CommunityBot | ||
| S Nov 2, 2022 at 23:08 | history | notice removed | CommunityBot | ||
| Oct 27, 2022 at 5:28 | comment | added | A. J. Pan-Collantes | Yes, I mean foliations which are described, locally, by a constant rank involutive distribution. This excludes "singular foliations", which are described by submodules of $\mathfrak X(M)$ whose rank can "go down" in some points (the singular points). | |
| Oct 26, 2022 at 22:40 | comment | added | Matthew Kvalheim | @TomGoodwillie by “regular” I mean that the leaves of the foliation have constant dimension, i.e. the foliation comes from an involutive tangent subbundle via the Frobenius theorem. That is the case I am interested in. I am guessing that what A.J. means by “regular point” is that leaves have constant dimension in a neighborhood of that point. | |
| Oct 26, 2022 at 20:29 | comment | added | Tom Goodwillie | "Regular" in what sense? | |
| Oct 26, 2022 at 19:38 | comment | added | A. J. Pan-Collantes | That's the point, I think I can prove a local result for regular points... | |
| Oct 26, 2022 at 18:56 | history | edited | Matthew Kvalheim | CC BY-SA 4.0 |
edited body
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| Oct 26, 2022 at 18:56 | comment | added | Matthew Kvalheim | @A.J.Pan-Collantes I am indeed assuming a regular foliation, but I would like to know a "global" answer to my question. (I already know how to produce at least one "local" result.) | |
| Oct 26, 2022 at 17:25 | comment | added | A. J. Pan-Collantes | Are you assuming a regular foliation? Are you ok with a "local result"? | |
| Oct 26, 2022 at 13:24 | comment | added | Matthew Kvalheim | @user126154 thanks - I clarified in Edit 2. | |
| Oct 26, 2022 at 13:23 | comment | added | Matthew Kvalheim | @TomGoodwillie thanks - I added Edit 1 with an explanation. | |
| Oct 26, 2022 at 13:23 | history | edited | Matthew Kvalheim | CC BY-SA 4.0 |
Edits made in response to comments
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| Oct 26, 2022 at 10:30 | comment | added | user126154 | I think you should specify better what exactly you are esking for: you say that you would like "a proof, specific reference of a counterexample". Which is the exact statement you would like to be proved or disproved? | |
| Oct 26, 2022 at 0:15 | comment | added | Tom Goodwillie | Each leaf of a foliation admits a manifold structure such that the inclusion into $M$ is a one-to-one immersion. What do you mean by "weakly embedded submanifold" or "weakly embedded initial submanifold"? | |
| Oct 25, 2022 at 21:52 | history | edited | Matthew Kvalheim | CC BY-SA 4.0 |
edited title
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| S Oct 25, 2022 at 21:30 | history | bounty started | Matthew Kvalheim | ||
| S Oct 25, 2022 at 21:30 | history | notice added | Matthew Kvalheim | Draw attention | |
| Oct 23, 2022 at 21:12 | history | asked | Matthew Kvalheim | CC BY-SA 4.0 |