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

2021/02/22 by Zipei Nie, Nie, Zipei
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2102.10891

openalex publication_date 2021/02/22 · openalex created_date 2021/03/01 · openalex updated_date 2026/07/28

Abstract

Greene, Lewallen and Vafaee characterized (1,1) L-space knots in S³ 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 S³ has non-left-orderable fundamental group.

Citations

• On 1-bridge braids, satellite knots, the manifold v2503 and non-left-orderable surgeries and fillings

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