Applications of a computer implementation of Poincaré’s theorem on fundamental polyhedra

  title={Applications of a computer implementation of Poincar{\'e}’s theorem on fundamental polyhedra},
  author={Robert F. Riley},
  journal={Mathematics of Computation},
PoincarCs Theorem asserts that a group F of isometries of hyperbolic space H is discrete if its generators act suitably on the boundary of some polyhedron in H, and when this happens a presentation of F can be derived from this action. We explain methods for deducing the precise hypotheses of the theorem from calculation in F when F is "algorithmi- cally defined", and we describe a file of Fortran programs that use these methods for groups F acting on the upper half space model of hyperbolic 3… 

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