Timeline for Finite covers of hyperbolic surfaces and the `second systole´
Current License: CC BY-SA 3.0
12 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Mar 15, 2017 at 16:35 | vote | accept | rpotrie | ||
| Mar 15, 2017 at 9:55 | answer | added | HJRW | timeline score: 5 | |
| Mar 15, 2017 at 2:39 | comment | added | rpotrie | @HJRW Yes, that would be great! Even if you don't get to where we want, explaining that a bit more would help. | |
| Mar 14, 2017 at 22:38 | comment | added | HJRW | I can construct a cover with the property that only lifts of your favouite curve have length $\ell$, and all other sccs have length greater than any fixed $K$. It should be relatively easy to get from there to what you want. I'll try to work out the details in the morning. | |
| Mar 14, 2017 at 10:27 | history | edited | rpotrie |
edited tags
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| Mar 14, 2017 at 0:55 | comment | added | rpotrie | Correct. I just edited to emphasise that. Thanks!. | |
| Mar 14, 2017 at 0:55 | history | edited | rpotrie | CC BY-SA 3.0 |
added 293 characters in body
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| Mar 14, 2017 at 0:49 | comment | added | Igor Rivin | Yes, that's right, I was asleep, BUT I believe that what I said makes sense for regular covers. | |
| Mar 14, 2017 at 0:34 | comment | added | rpotrie | @IgorRivin The unique (simple closed) geodesic of length $\leq \ell$ is in $\hat S$, so it projects to some curve $\gamma$ of length $\leq \ell$ in $S$. Clearly, the preimage of $\gamma$ by $p$ has many other preimages which are longer than $K$ in addition to the 'short' one. For other curves of length $\leq K$ in $S$ different from $\gamma$, \textit{all} the preimages in $\hat S$ must have length $\geq K$. Did I understand right? | |
| Mar 13, 2017 at 23:37 | comment | added | Igor Rivin | I am a little confused. If there is a unique geodesic of length $\leq \ell,$ then what exactly would cover it? Either the cover is connected (so you lose $\leq \ell,$ or not, so you lose uniqueness. Am I missing something? | |
| Mar 13, 2017 at 20:02 | history | asked | rpotrie | CC BY-SA 3.0 |