An Elementary Approach on Left-Orderability, Cables of Torus Knots and Dehn Surgery

Jianhui Li; Chun-Yin Siu

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arXiv · 1610.00898

An Elementary Approach on Left-Orderability, Cables of Torus Knots and Dehn Surgery

Jianhui Li·Chun-Yin Siu

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Abstract

Motivated by Clay and Watson's question on left-orderability of the fundamental group of the resultant space of an $r'$-surgery on the $(p, q)$-cable knots for $r' \in (pq-p-q,pq)$, this paper proves by elementary means that for specific pairs of $(p,q)$-cable knots of torus knots, $r' \in [pq-1,pq]$ gives a surgery yielding non-left orderable fundamental groups.

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Jianhui Li, Chun-Yin Siu. 2016-10-04. An Elementary Approach on Left-Orderability, Cables of Torus Knots and Dehn Surgery. https://arxiv.org/abs/1610.00898

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