Ying Hu
Published 2013-11-13, updated 2014-07-01Version 3
We provide an alternative proof of a sufficient condition for the fundamental group of the $n^{th}$ cyclic branched cover of $S^3$ along a prime knot $K$ to be left-orderable, which is originally due to Boyer-Gordon-Watson. As an application of this sufficient condition, we show that for any $(p,q)$ two-bridge knot, with $p\equiv 3 \text{ mod } 4$, there are only finitely many cyclic branched covers whose fundamental groups are not left-orderable. This answers a question posed by D{\c a}bkowski, Przytycki and Togha.
Comments: 13 pages, 2 figures; the abstract and introduction are substantially revised from the previous version; a mathematical typo is corrected in section 4;
Four-manifolds of large negative deficiency
Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links
Three manifold groups, Kaehler groups and complex surfaces
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