Convex foliated projective structures and the hitchin component for PSL4(R)

摘要

In this article, we give a geometric interpretation of the Hitchin component C Rep(pi(1),(Sigma), PSL4(R)) of a closed oriented stafiice of genus g >= 2. We show that representations in J-4 (Sigma) are, precisely, the holonomy representations (if properly convex foliated projective structures on the unit tangent bundle of Sigma. From this, we also deduce a geometric description of the Hitchin component J(Sigma, SP4(R)) of representations into the symplectic group.