论文标题
4球中的Seifert表面
Seifert surfaces in the 4-ball
论文作者
论文摘要
我们从1982年开始的利文斯顿（Livingston）回答了一个与$ s^3 $结的同一属的Seifert表面，当将其内部室内推入$ b^4 $时，它们不会成为同位素。特别是，我们确定表面在$ b^4 $中甚至没有拓扑同位素的示例，在拓扑上但不是同位素平稳的示例，以及无限表面家族的示例，这些示例只能与同位素相关。边界。我们的主要证明使用Khovanov同源性的COBORDISM图来区分表面，我们的计算证明了在某些卫星操作下这些地图的稳定性和可计算性。
We answer a question of Livingston from 1982 by producing Seifert surfaces of the same genus for a knot in $S^3$ that do not become isotopic when their interiors are pushed into $B^4$. In particular, we identify examples where the surfaces are not even topologically isotopic in $B^4$, examples that are topologically but not smoothly isotopic, and examples of infinite families of surfaces that are distinct only up to isotopy rel. boundary. Our main proofs distinguish surfaces using the cobordism maps on Khovanov homology, and our calculations demonstrate the stability and computability of these maps under certain satellite operations.
