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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