论文标题
一个无限的反示例家族，是巴特森的猜想
An infinite family of counterexamples to Batson's conjecture
论文作者
论文摘要
Batson的猜想是Milnor的猜想的不可取向版本，该版本指出，圆环结的4球属$ t（p，q）$等于$ \ frac {（p-1）（q-1）（q-1）} {2} $。巴特森的猜想指出，不可定向的4球属等于圆环结的捏合数，即获得未开关所需的特定类型（不可方向的）带手术的数量。最近，Lobb证明了猜想是错误的。我们将证明Lobb的反例适合无限的反例。
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.
