Symmetries of hyperbolic 4-manifolds
Alexander Kolpakov, Leone Slavich

TL;DR
This paper constructs explicit examples of hyperbolic 4-manifolds with prescribed finite symmetry groups using Coxeter polytopes and simplicial complex combinatorics, advancing the understanding of symmetries in hyperbolic geometry.
Contribution
It provides explicit constructions of hyperbolic 4-manifolds with any given finite symmetry group, combining geometric and combinatorial methods.
Findings
Explicit hyperbolic 4-manifolds with prescribed symmetry groups
Use of Coxeter polytopes in construction
Application of simplicial complex combinatorics
Abstract
In this paper, for each finite group , we construct explicitly a non-compact complete finite-volume arithmetic hyperbolic -manifold such that , or . In order to do so, we use essentially the geometry of Coxeter polytopes in the hyperbolic -space, on one hand, and the combinatorics of simplicial complexes, on the other.
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