Reference : Revisiting Poincaré's Theorem on presentations of discontinuous groups via fundamenta... |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/45737 | |||

Revisiting Poincaré's Theorem on presentations of discontinuous groups via fundamental polyhedra | |

English | |

Jespers, E. [> >] | |

Kiefer, Ann [University of Luxembourg > Faculty of Humanities, Education and Social Sciences (FHSE) > LUCET] | |

del Río, Á. [> >] | |

2015 | |

Expositiones Mathematica | |

33 | |

4 | |

401--430 | |

Yes (verified by ORBi^{lu}) | |

0723-0869 | |

[en] Discontinuous groups ; Kleinian Groups ; Presentations ; Fundamental Domain | |

[en] We give a new self-contained proof of Poincaré's Polyhedron Theorem on presentations of discon-
tinuous groups of isometries of a Riemann manifold of constant curvature. The proof is not based on the theory of covering spaces, but only makes use of basic geometric concepts. In a sense one hence obtains a proof that is of a more constructive nature than most known proofs. | |

http://hdl.handle.net/10993/45737 |

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