2008/06/25 by Michael Farber, Farber, Michael, Mark Grant +1 · 1 citation
Mathematics · #55M99 #55R80 #68T40. #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55M99 #msc:55R80 #msc:68T40.
paper · pdf · doi:10.48550/arxiv.0806.4111
arxiv created 2008/06/25 · arxiv updated 2009/12/01
The topological complexity TC(X) is a homotopy invariant which reflects the complexity of the problem of constructing a motion planning algorithm in the space X, viewed as configuration space of a mechanical system. In this paper we complete the computation of the topological complexity of the configuration space of n distinct points in Euclidean m-space for all m>1 and n>1; the answer was previously known in the cases m=2 and m odd. We also give several useful general results concerning sharpness of upper bounds for the topological complexity.