Status
Completed

Period
16-25 March 2023

Applicant
Paolo Cavicchioli

Home Institution
Università degli studi di Modena e Reggio Emilia, Italy

Host Contact
Prof. Sofia Lambropoulou

Host Institution
National Technical University of Athens, Greece

Aim of the mission
The goal of the STSM is to solve the problem of braiding links in thickened surfaces and of the equivalence of plat closure of braids in handlebodies. These elements could help the computation of polynomial knots invariants, which are used in the braid representation of DNA and proteins.

Summary of the Results
We discussed a sketch of the proof of the two main results, solving the problems cited before, fixing the technical details and writing a draft of the research paper. Also, we wrote in pseudocode the algorithm which implements the theorem. The goal of this STSM was mostly achieved, obtaining useful results for the upcoming research part.

Dissemination
Prof. Lambropoulou presented our results at the online conference “Knots Algebra and Geometry” on the occasion of the 60th birthdays of Profs. Valeriy Bardakov and Andrei Vesnin, and we are presenting it also at the upcoming 2023 International Conference on Topology and its Applications in Nafpaktos. I also presented the results at the TGV seminar in Bologna (https://www.dm.unibo.it/~marco.moraschini2/TGV.html). After the STSM, we finished producing the research paper, and it is submitted for publication.