Infinitely many hyperbolic Coxeter groups through dimension 19
| dc.creator | Allcock, Daniel | |
| dc.date | 2009-03-01 | |
| dc.date | 2009-03-16 | |
| dc.date.accessioned | 2026-07-07T12:52:17Z | |
| dc.date.available | 2026-07-07T12:52:17Z | |
| dc.description | We prove the following: there are infinitely many finite-covolume (resp. cocompact) Coxeter groups acting on hyperbolic space H^n for every n < 20 (resp. n < 7). When n=7 or 8, they may be taken to be nonarithmetic. Furthermore, for 1 < n < 20, with the possible exceptions n=16 and 17, the number of essentially distinct Coxeter groups in H^n with noncompact fundamental domain of volume less than or equal to V grows at least exponentially with respect to V. The same result holds for cocompact groups for n < 7. The technique is a doubling trick and variations on it; getting the most out of the method requires some work with the Leech lattice. | |
| dc.description | This is the version published by Geometry & Topology on 11 July 2006 (V2: typesetting correction) | |
| dc.identifier | https://arxiv.org/abs/0903.0138 | |
| dc.identifier | http://arxiv.org/abs/0903.0138 | |
| dc.identifier | Geom. Topol. 10 (2006) 737-758 | |
| dc.identifier | doi:10.2140/gt.2006.10.737 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223250 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F55, 51M10, 51M20 | |
| dc.title | Infinitely many hyperbolic Coxeter groups through dimension 19 | |
| dc.type | text |