Affine laminations and coaffine representations

We study surface subgroups of SL(4, R) acting convex cocompactly on R P³ with image in the coaffine group. The boundary of the convex core is stratified, and the one dimensional strata form a pair of bending laminations. We show that the bending data on each component consist of a convex R P² structure and an affine measured lamination depending on the underlying convex projective structure on S with (Hitchin) holonomy ρ: π₁S → SL(3, R). We study the space ML^ρ(S) of bending data compatible with ρ and prove that its projectivization is a sphere of dimension $6g-7$.