2019/08/31 by Polletta, David
#22E40 (Primary) #32Q45 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1909.00251
Mark and Paupert devised a general method for obtaining presentations for arithmetic non-cocompact lattices, Γ, in isometry groups of negatively curved symmetric spaces. The method involves a classical theorem of Macbeath applied to a Γ-invariant covering by horoballs of the negatively curved symmetric space upon which Γ acts. In this paper, we will discuss the application of their method to the Picard modular groups, \textrmPU(2,1;Od), when d=2,11, and obtain presentations for these groups, which completes the list of presentations for Picard modular groups whose entries lie in Euclidean domains, namely those with d=1,2,3,7,11.