The Action of SL(2 , C) on Hyperbolic 3-Space and Orbital Graphs

Abstract

In this paper we discuss the action of SL(2 , C) on hyperbolic 3-space using quaternions. And then we investigate suborbital graphs for the special subgroup of PSL(2 , C). We point out the relation between elliptic elements and circuits in graphs. Results obtained by the method used are important because they mean that suborbital graphs have a potential to explain signature problems. © 2018, Springer Japan KK, part of Springer Nature.