Linear motion planning with controlled collisions and pure planar braids
Jesús González, José Luis León-Medina, Christopher Roque-Márquez
Abstract
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.
Topics & Concepts
BraidMathematicsBraid groupPlanarTopological complexityConfiguration spaceMotion (physics)Topology (electrical circuits)Motion planningBraid theoryGroup (periodic table)Pure mathematicsSpace (punctuation)CombinatoricsGeometric topologyDiscrete mathematicsFundamental groupAlgebra over a fieldTopological groupGroup theoryGeometric and Algebraic TopologyHomotopy and Cohomology in Algebraic TopologyAdvanced Combinatorial Mathematics