Symplectic geometry of projective structures on surfaces with boundary
Symplectic Geometry
2026-01-15 v1 Differential Geometry
Abstract
For oriented surfaces with boundary, we consider the infinite-dimensional deformation space of projective structures on 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.
Keywords
Cite
@article{arxiv.2601.09662,
title = {Symplectic geometry of projective structures on surfaces with boundary},
author = {Ahmadreza Khazaeipoul and Eckhard Meinrenken},
journal= {arXiv preprint arXiv:2601.09662},
year = {2026}
}