Motion planning in tori. (English) Zbl 1196.55021
Summary: 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.
MSC:
| 55R80 | Discriminantal varieties and configuration spaces in algebraic topology |
| 55M35 | Finite groups of transformations in algebraic topology (including Smith theory) |
| 20F36 | Braid groups; Artin groups |
| 52C35 | Arrangements of points, flats, hyperplanes (aspects of discrete geometry) |
| 70E60 | Robot dynamics and control of rigid bodies |
| 93C85 | Automated systems (robots, etc.) in control theory |
