Timeline for How to increase the injectivity radius function of a hyperbolic 3 manifold of finite volume?
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| Jul 14, 2016 at 6:18 | comment | added | Jean Raimbault | If you want estimates on the degree you can get a quantitative version of this using the proof of finite residuality. Namely, $\pi_1 N$ embeds in $SL(2,R)$ for some finitely generated integral domain $R$ (in this case it can be taken to be a ring of $S$-integers for some finite ser $S$). Then taking the covers corresponding to the morphisms $\pi_1 N \to SL_2(R/nR)$ for non-invertible integers $n \in R$ you get a sequence of manifolds with injectivity radius $\ge \epsilon \log n$ (the volume is of order some power of $n$). | |
| Jul 13, 2016 at 20:16 | history | edited | Neil Hoffman | CC BY-SA 3.0 |
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| Jul 12, 2016 at 17:53 | history | answered | Neil Hoffman | CC BY-SA 3.0 |