Orderable 3-manifold groups

Boyer, Steven; Rolfsen, Dale et Wiest, Bert (2005). « Orderable 3-manifold groups ». Annales de l’institut Fourier, 55(1), pp. 243-288.

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Résumé

We investigate the orderability properties of fundamental groups of 3-dimensional manifolds. Many 3-manifold groups support left-invariant orderings, including all compact P 2 -irreducible manifolds with positive first Betti number. For seven of the eight geometries (excluding hyperbolic) we are able to characterize which manifolds’ groups support a left-invariant or bi-invariant ordering. We also show that manifolds modelled on these geometries have virtually bi-orderable groups. The question of virtual orderability of 3-manifold groups in general, and even hyperbolic manifolds, remains open, and is closely related to conjectures of Waldhausen and others.

Type: Article de revue scientifique
Mots-clés ou Sujets: 3-manifold, orderable group, LO-group
Unité d'appartenance: Faculté des sciences > Département de mathématiques
Déposé par: Steven P. Boyer
Date de dépôt: 18 avr. 2016 17:19
Dernière modification: 27 avr. 2016 18:14
Adresse URL : http://www.archipel.uqam.ca/id/eprint/8174

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