Motion planning in tori

Mathematics – Geometric Topology

Scientific paper

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

Scientific paper

10.1112/blms/bdn005

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.

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