Infinitely many hyperbolic Coxeter groups through dimension 19

dc.creatorAllcock, Daniel
dc.date2009-03-01
dc.date2009-03-16
dc.date.accessioned2026-07-07T12:52:17Z
dc.date.available2026-07-07T12:52:17Z
dc.descriptionWe 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.descriptionThis is the version published by Geometry & Topology on 11 July 2006 (V2: typesetting correction)
dc.identifierhttps://arxiv.org/abs/0903.0138
dc.identifierhttp://arxiv.org/abs/0903.0138
dc.identifierGeom. Topol. 10 (2006) 737-758
dc.identifierdoi:10.2140/gt.2006.10.737
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223250
dc.subjectGroup Theory
dc.subjectGeometric Topology
dc.subject20F55, 51M10, 51M20
dc.titleInfinitely many hyperbolic Coxeter groups through dimension 19
dc.typetext

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