Title:

Fundamental domains for leftright actions in Lorentzian geometry

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 leftright 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 QGorenstein surface singularities, i.e. the intersections of the singular variety with suffi�ciently small spheres around the isolated singular point as shown in [16].
