Thin representations for the one-cone torus group

摘要

This is a sequel of the author's work which aims at extending Jorgensen's work on the once punctured torus to a torus with a cone point. This paper is devoted to a study of cone hyperbolic manifolds with "thin" holonomy representations. We give an explicit construction of such cone manifolds and the "convex cores" of such cone manifolds. We also give two natural parametrizations of such cone manifolds. (C) 2019 Elsevier B.V. All rights reserved.