Components of Hom(π1, PGL(2, R))

In Topological Components of Spaces of Representations [1] Goldman calculated the number of topological components of the varieties Hom(π1(M), PSL(2, R)) and Hom(π1(M), PSL(2,C)) where M is a compact Riemann surface of genus g > 1. In this paper, we analyze the variety Hom(π1(M), PGL(2, R)) and show that it has 22g + 1 + 4g − 5 connected components.