Density properties of Euler characteristic -2 surface group, PSL(2,R) character varieties.

Abstract

In 1981, Dr. William Goldman proved that surface group representations into PSL(2,R) admit hyperbolic structures if and only if their Euler class is maximal in the Milnor-Wood interval. Furthermore the mapping class group of the prescribed surface acts properly discontinuously on its set of extremal representations into PSL(2,R). However, little is known about either the geometry of, or the mapping class group action on, the other connected components of the space of surface group representations into PSL(2,R). This article is devoted to establishing a few results regarding this.