On extended link signatures

Livio Ferretti (University of Glasgow)

Monday 28th April 16:00-17:00 Maths 311B

Abstract

The multivariable signature is a link invariant constructed as a generalization of the classical Levine-Tristram signature. For a link with $n$ components, it is given by a function $(S^1\setminus \{1\})^n \rightarrow \mathbb{Z}$. The multivariable signature was recently extended by Cimasoni-Markiewicz-Politarczyk to a function defined on the full torus $(S^1)^n$. In this talk we will introduce this extended signature and discuss some of its properties, in particular concerning its concordance invariance and the relationship with the Alexander polynomial. Based on joint work with D. Cimasoni and I. Popova.

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