Extended signatures and link concordance

Article Article scientifique Article Extended signatures and link concordance eng 2025-09-02 author Cimasoni David https://orcid.org/0000-0002-1260-5985 95617 Section de mathématiques (MATH) author Ferretti Livio Clemente Emilio 823869 author Popova Iuliia 990150 10.1017/s0013091525101053 0013-0915 https://www.cambridge.org/core/product/identifier/S0013091525101053/type/journal_article The Levine–Tristram signature admits a <i>µ</i> -variable extension for <i>µ</i> -component links: it was first defined as an integer-valued function on $(S^1\setminus\{1\})^\mu$ , and recently extended to the full torus $\mathbb{T}^\mu$ . The aim of the present article is to study and use this extended signature. Firstly, we show that it is constant on the connected components of the complement of the zero locus of some renormalized Alexander polynomial. Then, we prove that the extended signature is a concordance invariant on an explicit dense subset of $\mathbb{T}^\mu$ . Finally, as an application, we present an infinite family of three-component links with the following property: these links are not concordant to their mirror image, a fact that can be detected neither by the non-extended signatures, nor by the multivariable Alexander polynomial, nor by the Milnor triple linking number. Dewey 510 25 Section de mathématiques 11 false Proceedings of the Edinburgh Mathematical Society fbc2f8df-76f6-4812-b90f-7f1201ef25dd Article (Published version) Public Article_scientifique_from_crossref.pdf 861638 application/pdf CC BY-4.0 5481d03c53139e5934ce693686da3a803c631052dbb4fc65966c6403e2f27ea4 openAccess Faculté des sciences / Section de mathématiques

Title	Published in	Year	Views	Downloads

Extended signatures and link concordance	Proceedings of the Edinburgh Mathematical Society	2025	17	164
A diagrammatic computation of abelian link invariants		2024	8	11

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