Left-orderable fundamental groups and Dehn surgery

Clay, A. and Watson, L. (2013) Left-orderable fundamental groups and Dehn surgery. International Mathematics Research Notices, 2013(12), pp. 2862-2890. (doi: 10.1093/imrn/rns129)

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It is well known that left-orderability of a group need not be preserved under quotients. As knot groups provide a natural class of left-orderable groups, this paper studies the following question: when is left-orderability preserved under the quotient associated with Dehn surgery? We establish a condition on peripheral elements that must hold whenever a given Dehn surgery yields a manifold with left-orderable fundamental group, leading to a workable criterion used to determine when sufficiently positive Dehn surgery produces manifolds with non-left-orderable fundamental group. We apply this criterion to a range of examples, all of which are L-space knots, and demonstrate that all sufficiently large surgeries have non-left-orderable fundamental group. This behavior is analogous to the property that sufficiently positive surgery on an L-space knot always yields an L-space.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Watson, Professor Liam
Authors: Clay, A., and Watson, L.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:International Mathematics Research Notices
Publisher:Oxford University Press
ISSN (Online):1687-0247

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