Work

Quadratic differentials and circle patterns on complex projective tori

Year: 2021

Type: article

Abstract: Given a triangulation of a closed surface, we consider a cross ratio system that assigns a complex number to every edge satisfying certain polynomial equations per vertex. Every cross ratio system induces a complex projective structure together with a circle pattern on the closed surface. In particular, there is an associated conformal structure. We show that for any triangulated torus, the projection from the space of cross ratio systems with prescribed Delaunay angles to the Teichmüller space is a covering map with at most one branch point. Our approach is based on a notion of discrete holomorphic quadratic differentials.

Source: Geometry & Topology

DOI: 10.2140/gt.2021.25.961

Author: Wai Yeung Lam

Institutions: University of Luxembourg, Brown University, Beijing Institute of Mathematical Sciences and Applications

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: Structures on Surfaces