# Hyperbolic cone-manifold structures with prescribed holonomy I: punctured tori

@article{Mathews2010HyperbolicCS,
title={Hyperbolic cone-manifold structures with prescribed holonomy I: punctured tori},
author={Daniel V. Mathews},
journal={Geometriae Dedicata},
year={2010},
volume={152},
pages={85-128}
}
• Daniel V. Mathews
• Published 2010
• Mathematics
• Geometriae Dedicata
• We consider the relationship between hyperbolic cone-manifold structures on surfaces, and algebraic representations of the fundamental group into a group of isometries. A hyperbolic cone-manifold structure on a surface, with all interior cone angles being integer multiples of 2π, determines a holonomy representation of the fundamental group. We ask, conversely, when a representation of the fundamental group is the holonomy of a hyperbolic cone-manifold structure. In this paper we prove results… CONTINUE READING

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