Symplectic geometry of projective structures on surfaces with boundary
Abstract
For oriented surfaces $Σ$ with boundary, we consider the infinite-dimensional deformation space of projective structures on $Σ$ 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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Advanced Differential Geometry Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 14 January 2026
- Document type
- Preprint