Multivariate Signatures of Iterated Torus Links

S. Yu. Orevkov

Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 1, pp. 73-92.

Résumé

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.

Détail

Keywords: multisignature, iterated torus link, splice diagram.

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