# Paolo Cavicchioli, Algorithms on knots and braids in R3 and 3-manifolds

Date of publication: 26. 11. 2023

Topology seminar

Monday

27

November

Time:

12:15 - 13:45

Location:

Predavalnica 3.06 in na spletu

The goal of this seminar is to present multiple algorithms dealing with knots and braids in 3-manifolds. More in detail, the first result will be about an algorithmic way of computing plat-slide moves for links in 3-manifolds admitting a Heegaard diagram of genus two and in two other families of 3-manifolds, i.e. Takahashi and Dunwoody manifolds. Then, given a knot or link in the form of plat closure of a braid, we describe an algorithm to obtain a braid representing the same knot or link but with the standard closure, and vice-versa. We analyse the three cases of knots and links in R3, in handlebodies and in thickened surfaces. For each algorithm, a sketch of the construction, proofs of the results and the calculation of the computational complexity will be presented.

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