传奇环和电缆链接

Pub Date : 2024-08-19 DOI:10.4310/jsg.2024.v22.n1.a2
Jennifer Dalton, John B. Etnyre, Lisa Traynor
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引用次数: 0

摘要

我们给出了 Legendrian 环链的分类。在此过程中,我们首次给出了链接的某些光滑对称性无法通过 Legendrian 同素异形实现的 Legendrian 链接无穷族的分类。我们还给出了第一个不可失稳但不具有最大瑟斯顿-贝内金不变式的链路族,并观察到了可以作为 Legendrian 环链路的分量来实现的 Legendrian 环结的奇特分布。对 Legendrian 环链的这种分类导致了对横向环链的分类。我们还给出了均匀稠密和 Legendrian 简单的结类型的 Legendrian 索链和横向索链的分类。在这里,我们看到了与 Legendrian 环链分类的一些相似之处,但也有一些不同之处。特别是,我们证明了在任何均匀稠结类型的索链中,都有一些 Legendrian 代表,对于这些索链,没有任何分量的对称性可以通过 Legendrian 等距来实现;在其他索链中,只有分量的循环排列可以实现;而在其他索链中,所有平滑对称性都可以实现。
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Legendrian torus and cable links
We give a classification of Legendrian torus links. Along the way, we give the first classification of infinite families of Legendrian links where some smooth symmetries of the link cannot be realized by Legendrian isotopies. We also give the first family of links that are non-destabilizable but do not have maximal Thurston–Bennequin invariant and observe a curious distribution of Legendrian torus knots that can be realized as the components of a Legendrian torus link. This classification of Legendrian torus links leads to a classification of transversal torus links. We also give a classification of Legendrian and transversal cable links of knot types that are uniformly thick and Legendrian simple. Here we see some similarities with the classification of Legendrian torus links but also some differences. In particular, we show that there are Legendrian representatives of cable links of any uniformly thick knot type for which no symmetries of the components can be realized by a Legendrian isotopy, others where only cyclic permutations of the components can be realized, and yet others where all smooth symmetries are realizable.
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