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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Abstract
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 |
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Status: | Published |
Refereed: | Yes |
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: | 1073-7928 |
ISSN (Online): | 1687-0247 |
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