# 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} }

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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