Linear motion planning with controlled collisions and pure planar braids

Jesús González, José Luis León-Medina, Christopher Roque-Márquez
2021 Homology, Homotopy and Applications  
We compute the Lusternik-Schnirelmann category (LS-cat) and higher topological complexity (TC s , s 2) of the "nok-equal" configuration space Conf (k) (R, n). With k = 3, this yields the LS-cat and the higher topological complexity of Khovanov's group PP n of pure planar braids on n strands, which is an R-analogue of Artin's classical pure braid group on n strands. Our methods can be used to describe optimal motion planners for PP n provided n is small. The second and third authors were
more » ... uthors were supported by a Conacyt scholarship and a Conacyt Postdoctoral Fellowship, respectively.
doi:10.4310/hha.2021.v23.n1.a15 fatcat:fbchkfobbbabjb7vbobcdgnfd4