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

Zipei Nie

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arXiv · 2102.10891

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

Zipei Nie

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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.

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Zipei Nie. 2021-02-22. An explicit description of $(1,1)$ L-space knots, and non-left-orderable surgeries. https://arxiv.org/abs/2102.10891

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