Symmetries of Tilings of Lorentz Spaces

Bin Turki, NI and Pratoussevitch, A ORCID: 0000-0003-2248-6382 (2020) Symmetries of Tilings of Lorentz Spaces. Moscow Mathematical Journal, 20 (2). pp. 257-276.

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Abstract

We study tilings of the 3-dimensional simply connected Lorentz manifold of constant curvature. This manifold is modelled on the Lie group equipped with the Killing form. The tilings are produced by the fundamental domain construction introduced by the second author. The construction gives Lorentz polyhedra as fundamental domains for the action by left multiplication of a discrete co-compact subgroup of finite level. We determine the symmetry groups of these tilings and discuss the connection with the Seifert fibration of the quotient space. We then give an explicit description of the symmetry group of the tiling in the case when the discrete subgroup is a lift of a triangle group.

Item Type:	Article
Uncontrolled Keywords:	Tilings, symmetries of tilings, Lorentz space forms, polyhedral fundamental domain, quasi-homogeneous singularity
Depositing User:	Symplectic Admin
Date Deposited:	28 Oct 2019 09:01
Last Modified:	19 Jan 2023 01:30
DOI:	10.17323/1609-4514-2020-20-2-257-276
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3023656