Symplectic geometry of projective structures on surfaces with boundary

2026/01/14 by Ahmadreza Khazaeipoul, Eckhard Meinrenken · 1 voice
Mathematics · #math.SG #math.DG

paper · pdf

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.

Citations

• The symplectic groupoid for the Adler-Gelfand-Dikii Poisson structure
• JT Gravity and the Ensembles of Random Matrix Theory
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• Moduli spaces of convex projective structures on surfaces
• Convex real projective structures on compact surfaces
• The Yang-Mills equations over Riemann surfaces
• Unitary representations of some infinite dimensional groups

Discussions

• Ahmadreza Khazaeipoul, Eckhard Meinrenken: Symplectic geometry of projective structures on surfaces with boundary https://arxiv.org/abs/2601.09662 https://arxiv.org/pdf/2601.09662 https://arxiv.org/ht [bsky, 0 points, 0 comments]

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