Timeline for Short basis in $\pi_1$ on a hyperbolic surface of bounded diameter
Current License: CC BY-SA 3.0
6 events
when toggle format | what | by | license | comment | |
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Mar 4, 2018 at 4:33 | history | edited | Ian Agol | CC BY-SA 3.0 |
added references.
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Mar 3, 2018 at 10:29 | vote | accept | aglearner | ||
Mar 3, 2018 at 10:27 | vote | accept | aglearner | ||
Mar 3, 2018 at 10:29 | |||||
Mar 3, 2018 at 1:42 | comment | added | Ian Agol | @aglearner: I think this might be more difficult (or rather, with worse bounds). Off the top of my head, I see how to get a bound which is of the form $dg^{Cg}$ for some constant $d$, which is superexponential. Extend the standard collection of loops to a triangulation with one vertex. Then one can change it to another triangulation with at most $C g\log g$ flips. Each flip changes the length by at most a factor of 2. See theorem 1.4 of this paper: arxiv.org/abs/1411.4285. I suspect one should be able to obtain better bounds though, maybe exponential (but I'm not conjecturing that)? | |
Mar 2, 2018 at 20:56 | comment | added | aglearner | Thank you! It looks indeed that this works. When I was asking the question I had in mind that this standard collection is the one from the very standard picture i.e. in $\pi_1(S,x)$ we have $[\gamma_1,\gamma_2]\cdot ...=1$ (like here: math.stackexchange.com/questions/479371/…). I wonder if your argument can be modified to give a good bound for this more restricted type of standard collections as well. | |
Mar 2, 2018 at 19:10 | history | answered | Ian Agol | CC BY-SA 3.0 |