Geodesic
Linear motion planning with controlled collisions and pure planar braids
Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 275-296.

Voir la notice de l'article provenant de la source International Press of Boston

We compute the Lusternik–Schnirelmann category (LS-cat) and higher topological complexity ($\operatorname{TC}_s, s \geqslant 2$) of the “no-$k$-equal” configuration space $\operatorname{Conf}^{(k)} (\mathbb{R}, n)$. With $k = 3$, this yields the LS-cat and the higher topological complexity of Khovanov’s group $\operatorname{PP}_n$ of pure planar braids on $n$ strands, which is an $\mathbb{R}$-analogue of Artin’s classical pure braid group on $n$ strands. Our methods can be used to describe optimal motion planners for $\operatorname{PP}_n$ provided $n$ is small.
DOI : 10.4310/HHA.2021.v23.n1.a15
Classification : 55M30, 55R80, 55S40, 68T40
Keywords: motion planning, higher topological complexity, sectional category, configuration space, controlled collision, pure planar braid 
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Jesús González; José Luis León-Medina; Christopher Roque-Márquez. Linear motion planning with controlled collisions and pure planar braids. Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 275-296. doi : 10.4310/HHA.2021.v23.n1.a15. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n1.a15/

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