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math.GT2023
The mixed Hilden braid group and the plat equivalence in handlebodies
Paolo Cavicchioli, Sofia Lambropoulou
Given a knot or link in the handlebody, , of genus we prove that it can always be represented as the plat closure of a braid in . We further establish the Hilden brai…
math.GT2023
A Markov theorem for plat closure of surface braids in Dunwoody and periodic Takahashi manifolds
Alessia Cattabriga, Paolo Cavicchioli
In this article we deal with the problem of finding equivalence moves for links in Dunwoody and periodic Takahashi manifolds. We represent these manifolds using Heegaard splitting…
math.GT2023
Passing from plat closure to standard closure of braids in , in handlebodies and in thickened surfaces
Paolo Cavicchioli, Sofia Lambropoulou
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 with the standard closure, and vice-versa…