Moduli spaces of real projective structures on surfaces: Notes on a paper by V.V. Fock and A.B. Goncharov

2018/01/11 by Alex Casella, Casella, Alex, Dominic Tate +3 · 2 citations
Mathematics · #20F65 #51A05 #51M10 #57M50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.1801.03913

openalex publication_date 2018/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These notes grew out of our learning and applying the methods of Fock and Goncharov concerning moduli spaces of real projective structures on surfaces with ideal triangulations. We give a self-contained treatment of Fock and Goncharov's description of the moduli space of framed marked properly convex projective structures with minimal or maximal ends, and deduce results of Marquis and Goldman as consequences. We also discuss the Poisson structure on moduli space and its relationship to Goldman's Poisson structure on the character variety.

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