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arXiv · 2601.09662

Symplectic geometry of projective structures on surfaces with boundary

Ahmadreza Khazaeipoul·Eckhard Meinrenken
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Abstract

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

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Ahmadreza Khazaeipoul, Eckhard Meinrenken. 2026-01-14. Symplectic geometry of projective structures on surfaces with boundary. https://arxiv.org/abs/2601.09662

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