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Bulletin of the London Mathematical Society Advance Access originally published online on March 31, 2008
Bulletin of the London Mathematical Society 2008 40(2):249-262; doi:10.1112/blms/bdn005
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© 2008 London Mathematical Society

Motion planning in tori

Daniel C. Cohen and Goderdzi Pruidze

Department of Mathematics Louisiana State University
Baton Rouge, LA 70808
USA
gio@math.lsu.edu
http://www.math.lsu.edu/~cohen
http://www.math.lsu.edu/~gio

Received 26 March 2007. Revision received 24 October 2007.

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.

The first author was partially supported by National Security Agency grant H98230 [GenBank] -05-1-0055.

2000 Mathematics Subject Classification 20F36, 52C35, 55M30.


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