论文标题
桥梁三口和Seifert固体
Bridge trisections and Seifert solids
论文作者
论文摘要
我们适应了Seifert的算法，用于经典结，并链接到四个球体中桥梁三裂表面的三平面图设置。我们的方法允许构建由Heegaard图描述的Seifert固体。可以认为所产生的固体具有可以在没有3柄的情况下建造的外部。相比之下，我们举例说明了塞弗固体（不是来自我们的结构）的示例，这些固体需要任意许多3处理器。我们以两个分类结果得出结论。第一个表明，承认双标准阴影图的表面没有打结。第二个说，某些扇区包含至少$ b-1 $补丁的A $ b $桥梁的三角形是完全可分解的，因此相应的表面没有打结。这肯定地解决了第二和第四作者的猜想。
We adapt Seifert's algorithm for classical knots and links to the setting of tri-plane diagrams for bridge trisected surfaces in the 4-sphere. Our approach allows for the construction of a Seifert solid that is described by a Heegaard diagram. The Seifert solids produced can be assumed to have exteriors that can be built without 3-handles; in contrast, we give examples of Seifert solids (not coming from our construction) whose exteriors require arbitrarily many 3-handles. We conclude with two classification results. The first shows that surfaces admitting doubly-standard shadow diagrams are unknotted. The second says that a $b$-bridge trisection in which some sector contains at least $b-1$ patches is completely decomposable, thus the corresponding surface is unknotted. This settles affirmatively a conjecture of the second and fourth authors.
