Quaternionic Fenchel-Nielsen coordinates

Krishnendu Gongopadhyay (IISER Mohali)

Abstract

In this talk we shall discuss a classification of pairs of loxodromic elements in Sp(2,1). This is a counterpart of the classification of (0, 3) sunbgroups of SL(2, R) that provided the Fenchel-Nielsen coordinates on the Teichmuller space. In this case, Sp(2,1) is the isometry group of the quaternionic hyperbolic plane and this classification should provide some degrees of freedom for conjugacy classes of discrete, faithful, totally loxodromic representations of a surface group into Sp(2,1).