An explicit description of $(1,1)$ L-space knots, and non-left-orderable surgeries

Zipei Nie

An explicit description of $(1,1)$ L-space knots, and non-left-orderable surgeries

Geometric Topology 2021-02-23 v1

Authors: Zipei Nie

Abstract

Greene, Lewallen and Vafaee characterized $(1,1)$ L-space knots in $S^3$ and lens space in the notation of coherent reduced $(1,1)$ -diagrams. We analyze these diagrams, and deduce an explicit description of these knots. With the new description, we prove that any L-space obtained by Dehn surgery on a $(1,1)$ -knot in $S^3$ has non-left-orderable fundamental group.

Keywords

l-space knots (1,1)-knots dehn surgery non-left-orderable fundamental group lens spaces coherent reduced diagrams

Cite

@article{arxiv.2102.10891,
  title  = {An explicit description of $(1,1)$ L-space knots, and non-left-orderable surgeries},
  author = {Zipei Nie},
  journal= {arXiv preprint arXiv:2102.10891},
  year   = {2021}
}

Comments

11 pages, 4 figures

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