On L-spaces and left-orderable fundamental groups

Boyer, S., Gordon, C.M. and Watson, L. (2013) On L-spaces and left-orderable fundamental groups. Mathematische Annalen, 356(4), pp. 1213-1245. (doi: 10.1007/s00208-012-0852-7)

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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 leftorderable 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).

Item Type:Articles
Glasgow Author(s) Enlighten ID:Watson, Professor Liam
Authors: Boyer, S., Gordon, C.M., and Watson, L.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematische Annalen
ISSN (Online):1432-1807

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