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

Jianhui Li; Chun-Yin Siu

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

Geometric Topology 2016-10-17 v3

Authors: Jianhui Li , Chun-Yin Siu

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.

Keywords

left-orderability cable knots torus knots Dehn surgery fundamental group

Cite

@article{arxiv.1610.00898,
  title  = {An Elementary Approach on Left-Orderability, Cables of Torus Knots and Dehn Surgery},
  author = {Jianhui Li and Chun-Yin Siu},
  journal= {arXiv preprint arXiv:1610.00898},
  year   = {2016}
}

Comments

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

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

Abstract

Keywords

Cite

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