Timeline for Fundamental group of an hyperbolic $4$-manifold
Current License: CC BY-SA 3.0
5 events
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| Oct 7, 2013 at 8:43 | comment | added | Misha | @IanAgol: Very true. To be honest, I do not know in details how the algorithm of Cartwright and Steger works. They first find a Siegel domain (using reduction theory) which contains the actual fundamental domain, but is typically larger. Then they somehow shop off some of its pieces until they get the actual fundamental domain. | |
| Oct 7, 2013 at 0:18 | comment | added | Ian Agol | One comment, Misha. If you choose an ordering on the elements, and find a finite-sided polyhedron satisfying Poincare's polyhedron theorem, then you don't necessarily know that those elements generate $\Gamma$, just a finite-index subgroup. Since the question asks about congruence arithmetic groups, in principle one could use number-theoretic formulae for the covolume of $\Gamma$ to find the index of the subgroup (one need not compute the covolume, just the Euler characteristic in dim 4). Then you keep going until you find a subgroup of index 1. | |
| Oct 6, 2013 at 22:55 | comment | added | Sasha Anan'in | Thanks Misha! This is not just an answer but also a few important problems. | |
| Jun 4, 2013 at 13:21 | vote | accept | Selim G | ||
| Jun 4, 2013 at 12:17 | history | answered | Misha | CC BY-SA 3.0 |