An algorithmic method to compute plat-like Markov moves in genus two 3-manifolds
Data: 09 MAGGIO 2023 dalle 11:15 alle 13:00
Luogo: Aula Bombelli, ore 11:15
Abstract: The study of equivalence of links represented by plat closures of braids dates back to Birman's article of 1976. Since then, numerous studies have been carried out to generalize her result to the case of links in 3-manifolds.
The aim of this talk is to define the equivalence moves of links in 3-manifolds of Heegaard genus two and to describe an algorithm that computes these moves automatically.
The talk will be divided into two parts:
• In the first part, we start with an introduction on Heegaard diagrams of 3-manifolds, the braid group and the equivalence theorem from Birman. Afterwards, we will construct the result for 3-manifolds and provide some examples for 3-manifolds of Heegaard genus one (i.e. lens spaces).
• In the second half, after recalling some definitions from graph theory, we will give some results concerning the representation of Heegaard diagrams from 6-tuples of integers describing coloured graphs on the edges. Starting from this combinatorial description, we will give a sketch of the proof of the main result of the talk. I will then discuss the possible research directions that have been followed and the future ones.