Abstract

We compute the multivariate signatures of any Seifert link (that is, a union of some fibers in a Seifert homology sphere), in particular, of the union of a torus link with one or both of its cores (cored torus link). The signatures of cored torus links are used in the Degtyarev–Florens–Lecuona splicing formula for computing multivariate signatures of cables over links. We use Neumann’s computation of equivariant signatures of such links.

For signatures of torus links with core(s), we also rewrite Neumann’s formula in terms of integral points in a certain parallelogram, similarly to Hirzebruch’s formula for signatures of torus links (without cores) via integral points in a rectangle.

中文翻译：

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迭代环面链接的多元签名

摘要

我们计算任何 Seifert 链接（即 Seifert 同源球中一些纤维的并集）的多元签名，特别是环面链接与其一个或两个核心（有芯环面链接）的并集。Degtyarev–Florens–Lecuona 拼接公式中使用了有芯环面链路的特征，用于计算链路上电缆的多元特征。我们使用 Neumann 计算此类链接的等变签名。

对于有核的环面链的签名，我们还根据某个平行四边形中的积分点重写了诺依曼公式，类似于 Hirzebruch 的通过矩形中积分点的环面链（无核）签名的公式。