From angled triangulations to hyperbolic structures

@article{Futer2010FromAT,
  title={From angled triangulations to hyperbolic structures},
  author={David Futer and Franccois Gu'eritaud},
  journal={arXiv: Geometric Topology},
  year={2010}
}
This survey paper contains an elementary exposition of Casson and Rivin's technique for finding the hyperbolic metric on a 3-manifold M with toroidal boundary. We also survey a number of applications of this technique. The method involves subdividing M into ideal tetrahedra and solving a system of gluing equations to find hyperbolic shapes for the tetrahedra. The gluing equations decompose into a linear and non-linear part. The solutions to the linear equations form a convex polytope A. The… 

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