Left-orderability and cyclic branched coverings

Abstract

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.

13 pages, 2 figures; the abstract and introduction are substantially revised from the previous version; a mathematical typo is corrected in section 4;

References in corpus (2)

• Graph manifolds, left-orderability and amalgamation
• Non-left-orderable double branched coverings

Cited by in corpus (6)

• Branched covers of quasipositive links and L-spaces
• Orderability and Dehn filling
• Links all of whose cyclic branched covers are L-spaces
• Bi-twist manifolds and two-bridge knots
• A unified Casson-Lin invariant for the real forms of SL(2)
• Circular orderability of 3-manifold groups