Thin hyperbolic reflection groups
| Autor: | Bogachev, Nikolay, Kolpakov, Alexander |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study a family of Zariski dense finitely generated discrete subgroups of $\mathrm{Isom}(\mathbb{H}^d)$, $d \geqslant 2$, defined by the following property: any group in this family contains at least one reflection in a hyperplane. As an application we obtain a general description of all thin hyperbolic reflection groups. In particular, we show that the Vinberg algorithm applied to a non-reflective Lorentzian lattice gives rise to an infinite sequence of thin reflection subgroups in $\mathrm{Isom}(\mathbb{H}^d)$, for any $d \geqslant 2$. Moreover, every such group is a subgroup of a group produced by the Vinberg algorithm applied to a Lorentzian lattice independently on the latter being reflective. As a consequence, all thin hyperbolic reflection groups are enumerable. Comment: 10 pages, 1 figure, revision and generalization |
| Databáze: | arXiv |
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