Quasi-arithmeticity of lattices in PO(n,1)

Scott Thomson

doi:10.1007/s10711-015-0092-6

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arXiv · 1412.4961

Quasi-arithmeticity of lattices in PO(n,1)

Scott Thomson

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Abstract

We show that the non-arithmetic lattices in PO(n,1) of Belolipetsky and Thomson (2011), obtained as fundamental groups of closed hyperbolic manifolds with short systole, are quasi-arithmetic in the sense of Vinberg, and, by contrast, the well-known non-arithmetic lattices of Gromov and Piatetski-Shapiro are not quasi-arithmetic. A corollary of this is that there are, for all $n\geq 2$, non-arithmetic lattices in PO(n,1) that are not commensurable with the Gromov--Piatetski-Shapiro lattices.

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Scott Thomson. 2014-12-16. Quasi-arithmeticity of lattices in PO(n,1). https://doi.org/10.1007/s10711-015-0092-6

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