Reference : Revisiting Poincaré's Theorem on presentations of discontinuous groups via fundamenta...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Revisiting Poincaré's Theorem on presentations of discontinuous groups via fundamental polyhedra
Jespers, E. mailto [> >]
Kiefer, Ann mailto [University of Luxembourg > Faculty of Humanities, Education and Social Sciences (FHSE) > LUCET]
del Río, Á. mailto [> >]
Expositiones Mathematica
Yes (verified by ORBilu)
[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.

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