Timeline for is there a criterion for a two-generator subgroup of $PL(2,K)$ to be a cocompact lattice?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 28, 2016 at 11:04 | comment | added | Venkataramana | If this is what you want to know, that should be your question: how to prove that the element $\gamma$ has its eigenvalues in $K$? The proof is the same as for reals! | |
| Nov 6, 2015 at 9:49 | comment | added | Rupert | I would like to know how to prove that if $\gamma$ is an element of a torsion-free cocompact lattice in $PL(2,K)$ for $K$ a non-archimedean local field then the eigenvalues of $\gamma$ are in $K$. Ihara appears to make this claim in his article "Discrete subgroups of $PL(2,k_{\mathcal{P}})$. | |
| Nov 6, 2015 at 9:16 | comment | added | Rupert | Yes, I apologise, I think I was mistaken. I was told that there was a criterion like this in Beardon's book "The Geometry of Discrete Groups" but I am having difficulty locating any result like that in the book. | |
| Nov 5, 2015 at 18:30 | comment | added | Misha | I do not believe there is a criterion for $SO(n,1)$. There is a couple of semi-algorithms (for an arbitrary finite collection of elements of $SO(n,1)$). One of the two semi-algorithms is due to Troel Jorgensen. The second is a bit more complicated and is not in the literature; unlike Jorgensen's semi-algorithm, it applies to all real rank 1 noncompact simple Lie groups. | |
| Nov 5, 2015 at 12:26 | comment | added | Igor Rivin | I second the question! | |
| Nov 5, 2015 at 10:24 | comment | added | Venkataramana | what is this criterion for $SO(n,1)$ please? | |
| Nov 5, 2015 at 9:57 | history | asked | Rupert | CC BY-SA 3.0 |