Fundamental Domains in Lorentzian Geometry

Pratoussevitch, Anna ORCID: 0000-0003-2248-6382 (2003) Fundamental Domains in Lorentzian Geometry. Geom. Dedicata 126 (2007), 155-175, 126 (1). pp. 155-175.

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Abstract

We consider discrete subgroups Gamma of the simply connected Lie group SU~(1,1), the universal cover of SU(1,1), of finite level, i.e. the subgroup intersects the centre of SU~(1,1) in a subgroup of finite index, this index is called the level of the group. The Killing form induces a Lorentzian metric of constant curvature on the Lie group SU~(1,1). The discrete subgroup Gamma acts on SU~(1,1) by left translations. We describe the Lorentz space form SU~(1,1)/Gamma by constructing a fundamental domain F for Gamma. We want F to be a polyhedron with totally geodesic faces. We construct such F for all Gamma satisfying the following condition: The image of Gamma in PSU(1,1) has a fixed point u in the unit disk of order larger than the index of Gamma. The construction depends on the group Gamma and on the orbit Gamma(u) of the fixed point u.

Item Type:	Article
Additional Information:	16 pages with 5 figures; typos corrected; introduction completed
Uncontrolled Keywords:	math.DG, math.DG, 53C50 (Primary); 14J17, 32S25, 51M20, 52B10 (Secondary)
Depositing User:	Symplectic Admin
Date Deposited:	12 Apr 2016 11:10
Last Modified:	17 Dec 2022 01:14
DOI:	10.1007/s10711-006-9117-5
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3000467

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