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- Title
Symmetries of Hyperbolic 4-Manifolds.
- Authors
Kolpakov, Alexander; Slavich, Leone
- Abstract
In this paper, for each finite group GG, we construct the first explicit examples of non-compact complete finite-volume arithmetic hyperbolic 4-manifolds MM such that IsomM≅GIsomM≅G, or Isom+M≅GIsom+M≅G. In order to do so, we use essentially the geometry of Coxeter polytopes in the hyperbolic 4-space, on the one hand, and the combinatorics of simplicial complexes, on the other hand. This allows us to obtain a universal upper bound on the minimal volume of a hyperbolic 4-manifold realizing a given finite group GG as its isometry group in terms of the order of the group. We also obtain asymptotic bounds for the growth rate, with respect to volume, of the number of hyperbolic 4-manifolds having a finite group GG as their isometry group.
- Subjects
HYPERBOLIC functions; HYPERBOLOID structures; FINITE volume method; COXETER complexes; POLYTOPES
- Publication
IMRN: International Mathematics Research Notices, 2016, Vol 2016, Issue 9, p2677
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnv210