Topological Complexity of Configuration Spaces
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556KbAbstractIn this thesis we study the homotopy invariant TC(X); the topological complexity of a space X. This invariant, introduced by Farber in , was originally motivated by a problem in Robotics; the motion planning problem. either has small order or small cohomological dimension. We also apply the navigation functions technique introduced in  to the study of the topological complexity of projective and lens spaces. In particular, we introduce a class of navigation functions on projective and lens spaces. It is known () that the topological complexity of a real projective space equals one plus its immersion dimension. A similar approach to the immersion dimension of some lens spaces has been suggested in hermes scarf replica
. the stochastic behaviour of the topological complexity of Eilenberg MacLane spaces of type K(G, 1), where G is a right angled Artin group associated to a random graph.