首页/论文/2011.00122

arXiv 2011.001222020-11math.GT

An infinite family of counterexamples to Batson's conjecture

Vincent Longo

备注：: 10 pages, 8 figures

英文摘要：

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 $\frac{(p-1)(q-1)}{2}$. 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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