Left-orderability, branched covers and double twist knots

Turner, Hannah

doi:10.1090/proc/15269

Left-orderability, branched covers and double twist knots
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Proc. Amer. Math. Soc. 149 (2021), 1343-1358 Request permission

Abstract:

For some families of two-bridge knots, including double twist knots with genus at least four, we determine precisely the set of integers $n>1$ such that the fundamental group of the $n$-fold cyclic branched cover of the 3-sphere along these knots is left-orderable. There are knots, including the figure-eight knot, for which this set is empty. We give the first class of hyperbolic knots, not of this type, for which these integers can be completely determined.

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