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- W2004339916 abstract "Poincaréâs Theorem asserts that a group $Gamma$ of isometries of hyperbolic space $mathbb {H}$ is discrete if its generators act suitably on the boundary of some polyhedron in $mathbb {H}$, and when this happens a presentation of $Gamma$ can be derived from this action. We explain methods for deducing the precise hypotheses of the theorem from calculation in $Gamma$ when $Gamma$ is algorithmically defined, and we describe a file of Fortran programs that use these methods for groups $Gamma$ acting on the upper half space model of hyperbolic 3-space ${mathbb {H}^3}$. We exhibit one modest example of the application of these programs, and we summarize computations of repesentations of groups ${text {PSL}}(2,mathcal {O})$ where $mathcal {O}$ is an order in a complex quadratic number field." @default.
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- W2004339916 date "1983-01-01" @default.
- W2004339916 modified "2023-10-14" @default.
- W2004339916 title "Applications of a computer implementation of Poincaré’s theorem on fundamental polyhedra" @default.
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- W2004339916 doi "https://doi.org/10.1090/s0025-5718-1983-0689477-2" @default.
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