On Kashaev’s Signature Conjecture (Livio Ferretti, Université de Berne)

14.11.2019 14:15

The Levine-Tristram signature of a link L is an invariant given by a function \sigma_L:\mathbb{S}^1\to\mathbb{Z}. This invariant has many interesting properties and applications, and can be defined in a variety of ways. It is interesting to notice that all those definitions are strongly topological, and, to the best of our knowledge, combinatorial interpretations of the signature only exist for the value at some specific points of the unit circle. In 2018, Kashaev defined a new matrix associated to any link diagram and proved how to extract an invariant from it, conjecturally equal to the Levine-Tristram signature (then conjecturally providing a first combinatorial definition of \sigma_L). In this talk we will first recall the definition and some basic properties of the Levine-Tristram signature, then construct Kashaev’s matrix and finally present some partial results that provide strong evidence for the conjecture. Joint with David Cimasoni.

Lieu

Room 623, Séminaire "Topologie et Géométrie"

Organisé par

Section de mathématiques

Intervenants

Livio Ferretti, Université de Berne

entrée libre

Classement

Catégorie: Séminaire