On L-spaces and left-orderable fundamental groups

Boyer, Steven; Gordon, C. McA. et Watson, Liam (2013). « On L-spaces and left-orderable fundamental groups ». Mathematische Annalen, 356(4), pp. 1213-1245.

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Résumé

Examples suggest that there is a correspondence between L-spaces and three-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions for several large classes of manifolds. In particular, we prove that they are equivalent for any closed, connected, orientable, geometric three-manifold that is non-hyperbolic, a family which includes all closed, connected, orientable Seifert fibred spaces. We also show that they are equivalent for the twofold branched covers of non-split alternating links. To do this we prove that the fundamental group of the twofold branched cover of an alternating link is left-orderable if and only if it is a trivial link with two or more components. We also show that this places strong restrictions on the representations of the fundamental group of an alternating knot complement with values in Homeo+(S1)

Type: Article de revue scientifique
Mots-clés ou Sujets: Rational Homology Sphere, Heegaard Floer Homology, Character Variety ,Dehn Twist, Mapping Class Group, Fundamental Group, Klein Bottle, Cone Point, Simple Closed Curve, Twofold Cover, Euler Class, Boundary Arc, Solid Tori, Solid Torus, Exact Sequence
Unité d'appartenance: Faculté des sciences > Département de mathématiques
Déposé par: Steven P. Boyer
Date de dépôt: 27 avr. 2016 13:39
Dernière modification: 19 mai 2016 18:00
Adresse URL : http://www.archipel.uqam.ca/id/eprint/8323

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