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Funktsional. Anal. i Prilozhen., 2021, Volume 55, Issue 1, Pages 73–92 (Mi faa3826)  

Multivariate Signatures of Iterated Torus Links

S. Yu. Orevkovabc

a Steklov Mathematical Institute, Moscow, Russia
b Institut de Mathématiques de Toulouse, l'Université Paul Sabatier, Toulouse, France
c Laboratory of Algebraic Geometry and Homological Algebra, Moscow Institute of Physics and Technology, Moscow, Russia

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.

Keywords: multisignature, iterated torus link, splice diagram.

DOI: https://doi.org/10.4213/faa3826

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English version:
Functional Analysis and Its Applications, 2021, 55:1, 59–74

Bibliographic databases:

UDC: 515.162.8
Received: 24.07.2020
Revised: 24.10.2020
Accepted:30.10.2020

Citation: S. Yu. Orevkov, “Multivariate Signatures of Iterated Torus Links”, Funktsional. Anal. i Prilozhen., 55:1 (2021), 73–92; Funct. Anal. Appl., 55:1 (2021), 59–74

Citation in format AMSBIB
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\by S.~Yu.~Orevkov
\paper Multivariate Signatures of Iterated Torus Links
\jour Funktsional. Anal. i Prilozhen.
\yr 2021
\vol 55
\issue 1
\pages 73--92
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\jour Funct. Anal. Appl.
\yr 2021
\vol 55
\issue 1
\pages 59--74
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