Left-orderable surgeries on the knot 6₂ via hyperbolic \widetildePSL(2,ℝ)-representations

2023/06/30 by Ollie Thakar, Thakar, Ollie
Mathematics · Medicine · #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2307.00107

openalex publication_date 2023/06/30 · openalex created_date 2023/07/05 · openalex updated_date 2026/07/28

Abstract

We introduce a new method of detecting when the fundamental group of a Dehn surgery on a knot admits a left-ordering, a method which is particularly useful for 2-bridge knots. As an illustration of this method, we show that all Dehn surgeries on the knot 6₂ with slope in the interval (-4, 8)∩ℚ have left-orderable fundamental groups by exhibiting a family of hyperbolic \widetildePSL(2,ℝ)-representations of the knot complement group.

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