On cabled knots, Dehn surgery, and left-orderable fundamental groups

Clay, A. and Watson, L. (2011) On cabled knots, Dehn surgery, and left-orderable fundamental groups. Mathematical Research Letters, 18(6), pp. 1085-1095. (doi: 10.4310/MRL.2011.v18.n6.a4)

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Publisher's URL: http://dx.doi.org/10.4310/MRL.2011.v18.n6.a4


Previous work of the authors establishes a criterion on the fundamental group of a knot complement that determines when Dehn surgery on the knot will have a fundamental group that is not left-orderable. We provide a refinement of this criterion by introducing the notion of a decayed knot; it is shown that Dehn surgery on decayed knots produces surgery manifolds that have non-left-orderable fundamental group for all sufficiently positive surgeries. As an application, we prove that sufficiently positive cables of decayed knots are always decayed knots. These results mirror properties of L-space surgeries in the context of Heegaard Floer homology.

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:Mathematical Research Letters
Publisher:International Press
ISSN (Online):1945-001X

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