Motion planning in tori

Abstract

Let X be a subcomplex of the standard CW-decomposition of the n-dimensional torus. We exhibit an explicit optimal motion planning algorithm for X. This construction is used to calculate the topological complexity of complements of general position arrangements and Eilenberg-Mac Lane spaces associated to right-angled Artin groups.

Results extended to arbitrary subcomplexes of tori. Results on products of even spheres added

References in corpus (3)

• Algebraic invariants for right-angled Artin groups
• Higher homotopy groups of complements of complex hyperplane arrangements
• Joins of DGA modules and sectional category

Cited by in corpus (7)

• Bredon cohomology and robot motion planning
• Geodesic complexity of motion planning
• Motion planning in spaces with small fundamental group
• Topological complexity of basis-conjugating automorphism groups
• Topological complexity of configuration spaces
• Sequential motion planning assisted by group actions
• New lower bounds for the topological complexity of aspherical spaces