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

@article{Clay2011OnCK,
title={On cabled knots, Dehn surgery, and left-orderable fundamental groups},
journal={arXiv: Geometric Topology},
year={2011}
}
• Published 1 March 2011
• Mathematics
• arXiv: Geometric Topology
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…
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