Test map and Discreteness in SL(2, \mathbb H)

2017/08/19 by Gongopadhyay, Krishnendu, Mukherjee, Abhishek, Sardar, Sujit Kumar
#20H25 #FOS: Mathematics #Geometric Topology (math.GT) #Primary 20H10 #Secondary 51M10

paper · doi:10.48550/arxiv.1708.05792

Abstract

Let SL(2, \mathbb H) be the group of 2 × 2 quaternionic matrices A=\beginpmatrix a & b c & d \endpmatrix with quaternionic determinant det A=|ad-aca^-1 b|=1. This group acts by the orientation-preserving isometries of the five dimensional (real) hyperbolic space. We obtain discreteness criteria for Zariski-dense subgroups of SL(2, \mathbb H) using test maps.

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