Fundamental domains for left-right actions in Lorentzian geometry

Bin Turki, Nasser Fundamental domains for left-right actions in Lorentzian geometry. PhD thesis, University of Liverpool.

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Abstract

We consider tilde{G} = tilde{SU}(1, 1) = tilde{SL}(2,R). The aim of this thesis is to compute the fundamental domains for two series of groups of the form tilde{Gamma}_1 X tilde{Gamma}_2 acting on tilde{G} by left-right multiplication,i.e. (g, h) . x = gxh^{−1}, where tilde{Gamma}_1 and tilde{Gamma}_2 are discrete subgroups of tilde{G} of the same finite level and tilde{Gamma}_2 is cyclic. The level of a subgroup tilde{Gamma} in tilde{G} is defined as the index of the group tilde{Gamma} intersection with Z(tilde{G}) in the center Z(tilde{G}) =� Z. From computing the fundamental domain we can describe the biquotients tilde{Gamma}_1 \ tilde{G} / tilde{Gamma}_2 which are diffeomorphic to the links of certain quasihomogeneous Q-Gorenstein surface singularities, i.e. the intersections of the singular variety with suffi�ciently small spheres around the isolated singular point as shown in [16].

Item Type:	Thesis (PhD)
Additional Information:	Date: 2014-10 (completed)
Subjects:	?? QA ??
Depositing User:	Symplectic Admin
Date Deposited:	26 Aug 2015 09:59
Last Modified:	17 Dec 2022 01:33
DOI:	10.17638/02003726
URI:	https://livrepository.liverpool.ac.uk/id/eprint/2003726