Symplectic geometry of projective structures on surfaces with boundary

Abstract

For oriented surfaces $\hat{I}\pounds$ with boundary, we consider the infinite-dimensional deformation space of projective structures on $\hat{I}\pounds$ with nondegenerate boundary, up to isotopies fixing the boundary. We show that this space carries a natural symplectic structure, and is a Hamiltonian space for the symplectic groupoid integrating the Adler-Gelfand-Dikii-space of the boundary.