2025/05/02 by François Guéritaud, Guéritaud, François, Pallavi Panda +1
Chemistry · Materials Science · #05E45 #53A35 #Advanced Polymer Synthesis and Characterization #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Organometallic Complex Synthesis and Catalysis #Synthesis and properties of polymers
paper · pdf · doi:10.48550/arxiv.2505.01285
openalex publication_date 2025/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study infinitesimal deformations of complete hyperbolic surfaces with boundary and with ideal vertices, possibly decorated with horoballs. ``Admissible'' deformations are the ones that pull all horoballs apart; they form a convex cone of deformations. We describe this cone in terms of the arc complex of the surface: specifically, this paper focuses on the surfaces for which that complex is finite. Those surfaces form four families: (ideal) polygons, once-punctured polygons, one-holed polygons (or ``crowns''), and Möbius strips with spikes. In each case, we describe a natural simplicial decomposition of the projectivised admissible cone and of each of its faces, realizing them as appropriate arc complexes.