The Torelli group and reducible representations to PSL(2,R)

Goldman Conjectured that for components of the PSL(2,R)-character variety of surface groups which do not contain holonomies of hyperbolic structures, the action by the mapping class group should be ergodic. Recently, March\'e and Wolff completely described the genus 2 case, wherein the euler number zero representations surprisingly split into two ergodic components. In new work with James Farre and Peter Smillie, we use a geometric interpretation of the tangent data to reducible representations within the euler class 0 component to give positive evidence towards Goldman's conjecture in the case where genus excedes two and euler number is zero.