In [8] Mostow constructed a family of lattices in PU(2, 1), the holomorphic isometry group of complex hyperbolic 2-space. These groups are special cases of the lattices constructed by Deligne and Mostow [2] using monodromy of hypergeometric functions. Thurston [12] reinterpreted the work of Deligne and Mostow in terms of cone metrics on the sphere. In this paper we use Thurston's point of view to give a direct construction of fundamental domains for Mostow's lattices. Our approach is a direct generalisation of Parker's construction for Livné's lattices [10]. The details may be found in Boadi's PhD thesis [1]. We note that Deraux, Falbel and Paupert [3] have also constructed fundamental domains for Mostow's groups. Our groups are different from the ones considered in the main part of [3].

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This paper focuses on the study of a one-dimensional topological dynamical system, the tent function. We give a good background to the theory of dynamical systems while establishing the important asymptotic properties of topological dynamical systems that distinguishes it from other fields by way of an example - the tent function. A precise definition of the tent function is given and iterates are clearly shown using the phase diagrams. By this same method, chaos in the tent map is shown as iterates become higher. We also show that the tent map has infinitely many chaotic orbits and also express some important features of chaos such as topological transitivity, boundedness and sensitivity to change in initial conditions from a topological viewpoint.

Abstract. In this paper we prove some trace identities in SL(3, C) and SU (2, 1) groups. We also present the merits on how to parametrise pair of pants via traces and cross-ratio. Finally, we compute traces of matrices that are generated by complex reflections in complex triangle groups.