Properties of extended link signatures (Iuliia Popova, Soutenance de Travail de Master)

27.06.2024 10:00

The multivariable signature is an extension of the Levine-Tristram signature for an oriented link to a \mu-colored link. Until recently, the multivariable signature was only defined on a \mu-torus without axes, that is on T^{\mu}_{*}:= (S^1 ∖ {1})^{\mu}, and it was not possible to extend it to the whole \mu-torus T^{\mu}:= (S^1)^{\mu} in the traditional 3-dimensional approach. In a recent article by Cimasoni, Markiewicz, and Politarczyk, the multivariable signature was extended to T^{\mu}, involving a 4-dimensional approach that redefines the signature through twisted homology. In this thesis, we explore the properties of the extended multivariable signature. Specifically, we prove its invariance under concordance, find a formula for evaluations on diagonals, and show that the extended signature is a stronger invariant than the non-extended signature and linking numbers.

Lieu

Bâtiment: Conseil Général 7-9

Room 6-13, Séminaire "Topologie et géométrie"

entrée libre