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

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.

11 pages, 4 figures

References in corpus (2)

• Floer Simple Manifolds and L-Space Intervals
• On $1$-bridge braids, satellite knots, the manifold $v2503$ and non-left-orderable surgeries and fillings