标题： 有限弧复形的多面体实现使用带变形 显示英文标题

标题： Polyhedral realisations of finite arc complexes using strip deformations

摘要： 我们研究了具有边界和理想顶点的完备双曲曲面的无穷小变形，可能还带有horoball装饰。 “允许”的变形是指那些将所有horoball分开的变形；它们构成了一个凸变形锥。 我们用曲面的弧复形来描述这个锥：具体地说，本文专注于那些其复形有限的曲面。 这些曲面分为四类：（理想）多边形、单点穿孔多边形、单孔多边形（或“王冠”）以及带有尖刺的Möbius带。 在每种情况下，我们都描述了投影化的允许锥及其每个面的自然单纯剖分，将其视为适当的弧复形。 显示英文摘要

摘要： 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 M\"obius 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.