论文标题
手柄 - 丝带结的等效表征
Equivalent characterizations of handle-ribbon knots
论文作者
论文摘要
稳定的考夫曼猜想认为，$ s^3 $中的结是切成薄片的，并且仅当它允许切片衍生物时。我们证明了一个相关的陈述：一个结是在同型4球$ b $的同型含量时（也称为强烈同型 - ribbon），并且仅当它允许R-link衍生物时；即$ n $ -component衍生$ l $，其财产为零框外科手术$ l $产量$ \＃^n（s^1 \ times s^2）$。我们还表明，$ k $在零件$ d \ subset b $时界限，并且仅当零手术在$ k $上获得的3个manifold承认了一种奇异的纤维，该振动在$ b \ setminus d $中延伸到手柄上，将Casson和Gordem的经典定理推广到Casson and Gordon案例中，以供无限制的人调用。
The stable Kauffman conjecture posits that a knot in $S^3$ is slice if and only if it admits a slice derivative. We prove a related statement: A knot is handle-ribbon (also called strongly homotopy-ribbon) in a homotopy 4-ball $B$ if and only if it admits an R-link derivative; i.e. an $n$-component derivative $L$ with the property that zero-framed surgery on $L$ yields $\#^n(S^1\times S^2)$. We also show that $K$ bounds a handle-ribbon disk $D \subset B$ if and only if the 3-manifold obtained by zero-surgery on $K$ admits a singular fibration that extends over handlebodies in $B \setminus D$, generalizing a classical theorem of Casson and Gordon to the non-fibered case for handle-ribbon knots.
