Timeline for Why a Teichmüller map is not a pseudo-Anosov?
Current License: CC BY-SA 4.0
18 events
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| S Dec 28, 2023 at 19:24 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
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| S Dec 28, 2023 at 19:24 | history | suggested | CommunityBot | CC BY-SA 4.0 |
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| Dec 28, 2023 at 18:11 | review | Suggested edits | |||
| S Dec 28, 2023 at 19:24 | |||||
| Dec 28, 2023 at 17:28 | answer | added | gaoqiang | timeline score: 0 | |
| Sep 13, 2022 at 9:11 | vote | accept | Andrey Ryabichev | ||
| Nov 10, 2020 at 16:15 | answer | added | Andrey Ryabichev | timeline score: 0 | |
| Nov 10, 2020 at 16:04 | comment | added | Andrey Ryabichev | @SamNead the Teichmuller existence theorem says that in any homotopy class of maps $X\to X$ there is a Teichmuller map. but the initial and terminal differentials for this Teichmuller map can be different up to isotopy, so there will be no pair of foliations with respect to which the map will be pseudo-anosov | |
| Nov 10, 2020 at 16:00 | comment | added | Andrey Ryabichev | @MoisheKohan okay, so this is an aswer. thank you! | |
| Nov 10, 2020 at 15:06 | comment | added | Moishe Kohan | @AndreyRyabichev Right. | |
| Nov 10, 2020 at 14:20 | answer | added | Sam Nead | timeline score: 1 | |
| Nov 10, 2020 at 14:15 | comment | added | Sam Nead | @AndreyRyabichev - That does not work. The Teichmuller map is required to be homotopic to the "change of marking" map. For an overview, see Section 11.1.3 of "A primer on mapping class groups". | |
| Nov 10, 2020 at 13:19 | comment | added | Andrey Ryabichev | @MoisheKohan in other words, $f$ may have initial differential $q_1$ and terminal differential $q_2$, which may not coincide, even up to isotopy (do i understand your argument correctly?) | |
| Nov 9, 2020 at 17:03 | comment | added | Moishe Kohan | Even if the map is from $X$ to itself, to be pA, it needs to preserve the vertical/horizontal foliations on $X$, while Teichmuller map only preserves them after you choose two sets of conformal coordinates on $X$ (regarded as both domain and the range of the map), effectively replacing $f$ with compositions $\phi \circ f \circ \psi$. This pre/post composition messes up VH foliations completely. | |
| Nov 9, 2020 at 15:04 | comment | added | Andrey Ryabichev | @SamNead i think we need to assume the markings for $X$ coincide, and $f$ to be the map not homotopic to identity | |
| Nov 9, 2020 at 14:02 | comment | added | Sam Nead | I think you may be confused. Usually, a Teichmuller map is between distinct (marked) Riemann surfaces, and not from a Riemann surface to itself. Perhaps you have two different markings on the given surface X? | |
| Nov 9, 2020 at 13:26 | history | edited | Andrey Ryabichev | CC BY-SA 4.0 |
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| Nov 9, 2020 at 13:18 | history | edited | Andrey Ryabichev | CC BY-SA 4.0 |
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| Nov 9, 2020 at 12:25 | history | asked | Andrey Ryabichev | CC BY-SA 4.0 |