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Given a knot or link in the form of plat closure of a braid, we describe analgorithm to obtain a braid representing the same knot or link with thestandard closure, and vice-versa. We analyze the three cases of knots andlinks: in \(\mathbb{R}^3\), in handlebodies and in thickened surfaces. We showthat the algorithm is quadratic in the number of crossings and loop generatorsof the braid when passing from plat to standard closure, while it is linearwhen passing from standard to plat closure.

Passing from plat closure to standard closure of braids in $\mathbb{R}^3$, in handlebodies and in thickened surfaces