Timeline for Foliations by circles on the 3-torus
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 14, 2017 at 16:45 | answer | added | rpotrie | timeline score: 1 | |
| Mar 10, 2017 at 19:33 | comment | added | GabrieleBenedetti | @RyanBudney: Thanks a lot for the reference. I had a look at Hatcher's notes. For him $T^3$ is the exceptional case $M_1$ on p.37, for which he does not seem to provide the isotopy classification (but maybe I am wrong). I also found Theorem 5.2 (originally due to Waldhausen) in these notes by Jankins and Neumann math.columbia.edu/~neumann/preprints/… which asserts that except some cases ($T^3$ is case iii) two homeomorphic Seifert fiberings are actually isotopic. | |
| Mar 10, 2017 at 19:16 | comment | added | GabrieleBenedetti | @johnmangual: I edited the question, so that now $\alpha$ is the isotopy class of the loop and not the homotopy class (maybe they are different and this could answer your point). | |
| Mar 10, 2017 at 19:14 | history | edited | GabrieleBenedetti | CC BY-SA 3.0 |
In this new version I strengthened one assumption.
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| Mar 9, 2017 at 21:16 | comment | added | Misha | The fact that circle foliations are Seifert fibrations (for arbitrary 3-manifold, even a noncompact one, and even without smoothness assumption) is due to D.B.A.Epstein "Periodic flows on 3-manifolds" Annals of Math, 1972. | |
| Mar 9, 2017 at 16:44 | review | First posts | |||
| Mar 9, 2017 at 16:55 | |||||
| Mar 9, 2017 at 16:31 | comment | added | Ryan Budney | A: Yes. Such foliations are Seifert fiberings, Using things like Alexander's theorem you can classify the the Seifert fiberings of manifolds that admit them, even up to isotopy. For example, take a look in Hatcher's 3-manifolds notes. | |
| Mar 9, 2017 at 16:19 | comment | added | john mangual | if the $S^1$ fibers tangle in any way, then I suspect they are not homotopic to the "trivial" foliation, $S^1 \times pt$. Is that right? | |
| Mar 9, 2017 at 16:10 | history | asked | GabrieleBenedetti | CC BY-SA 3.0 |