English

Symplectic geometry of projective structures on surfaces with boundary

Symplectic Geometry 2026-01-15 v1 Differential Geometry

Abstract

For oriented surfaces Σ\Sigma with boundary, we consider the infinite-dimensional deformation space of projective structures on Σ\Sigma 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}
}