An infinite family of counterexamples to Batson's conjecture

2020/10/30 by Vincent Longo, Longo, Vincent · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2011.00122

openalex publication_date 2020/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Batson's conjecture is a non-orientable version of Milnor's conjecture, which states that the 4-ball genus of a torus knot T(p,q) is equal to ((p-1)(q-1))/(2). Batson's conjecture states that the nonorientable 4-ball genus is equal to the pinch number of a torus knot, i.e. the number of a specific type of (nonorientable) band surgeries needed to obtain the unknot. The conjecture was recently proved to be false by Lobb. We will show that Lobb's counterexample fits into an infinite family of counterexamples.

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• The Non-Orientable Four-Ball Genus of a New Infinite Family of Torus Knots

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