Um domínio fundamental para o Grupo Modular de Eisentein-Picard agindo sobre o espaço hiperbólico complexo

Abstract

In this work, we study the Eisenstein-Picard Modular Group, ! = PU(2, 1, Z[w]), where FÓRMULA DISPONÍVEL NO TEXTO COMPLETO. This is a subgroup of biholomorphic isometries of the complex hyperbolic space, whose entries are in the ring Z[w]. Our goal is to construct a fundamental domain for the action of ! in H2 C and, as a consequence of this construction, obtain a presentation for !. There are several ways to obtain a fundamental domain for the action of a group on a particular space. One of them is by Dirichlet polyhedra. In our case, this is not the best way to obtain a fundamental domain, because it gives rise to combinatorially complicated objects.