Timeline for Codimension two foliations with transverse surfaces
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 4, 2021 at 21:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 4, 2021 at 20:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 7, 2020 at 19:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 7, 2020 at 18:47 | answer | added | Gael Meigniez | timeline score: 3 | |
| Aug 19, 2020 at 1:48 | comment | added | guest | Foliations transverse to the fibering of a fiber bundle with compact fiber, in any dimension and codimension, correspond to conjugacy classes of representations of $\pi_1(B)$, into $Homeo(F)$. Where $B$ is the base space and $F$ is the fiber. Let $\rho$ be such a representation, and let $\tilde{B}$ be the universal cover of $B$ and let $G = \{(\alpha, \rho(\alpha)\}$ where $\alpha$ ranges over $\pi_1(B)$. To construct the foliation, mod out $\tilde{B} \times F$ by $G$. The leaves descend from the product foliation of $\tilde{B} \times \{point\}$, and leafwise cover $B$ under bundle projection. | |
| Aug 19, 2020 at 0:51 | comment | added | Rohil Prasad | What is the classification in this case? | |
| Aug 19, 2020 at 0:37 | comment | added | guest | For the special case that $\Sigma$ is the fiber of a surface bundle structure for $X$, the foliations you ask about are completely classified. That probably barely scatches the surface of the problem though. | |
| Aug 18, 2020 at 23:55 | history | asked | Rohil Prasad | CC BY-SA 4.0 |