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

Abstract

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

7 pages; added subject classification and keywords, corrected a typo in v2; corrected a typo in v3