Arf invariants of colored links

25.05.2023 14:15

The Arf invariant is a modulo 2 integer associated to a non singular quadratic form over the field F_2. In 1965, Robertello applied this theory to Seifert forms, leading to an invariant of a certain class of oriented links. Colored links are a natural generalisation of oriented links, where the components are grouped into sublinks. Several invariants of oriented links, such as the Alexander module and the Levine-Tristram signature, admit natural multivariable extensions to colored links via so-called "generalised Seifert surfaces". In this talk, I will define these notions, and briefly explain how to use generalised Seifert surfaces to extend the Arf-Robertello invariant to colored links. Unfortunately, these extensions turn out to be determined by the linking numbers.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Topologie et géométrie"

entrée libre