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

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


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/45737

Title :	Revisiting Poincaré's Theorem on presentations of discontinuous groups via fundamental polyhedra
Language :	English
Author, co-author :	Jespers, E. [> >]
	Kiefer, Ann [University of Luxembourg > Faculty of Humanities, Education and Social Sciences (FHSE) > LUCET]
	del Río, Á. [> >]
Publication date :	2015
Journal title :	Expositiones Mathematica
Volume :	33
Issue/season :	4
Pages :	401--430
Peer reviewed :	Yes (verified by ORBi^lu)
ISSN :	0723-0869
Keywords :	[en] Discontinuous groups ; Kleinian Groups ; Presentations ; Fundamental Domain
Abstract :	[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.
Permalink :	http://hdl.handle.net/10993/45737

File(s) associated to this reference

Fulltext file(s):

	File	Commentary	Version	Size	Access
Limited access	JesKiedRioPoincare.pdf		Author postprint	393.43 kB	Request a copy

All documents in ORBi^lu are protected by a user license.