The Topological Complexity of a space has been introduced by M. Farber in the context of the study of the motion planning problem in robotics. It is, in general, difficult to calculate this numerical homotopy invariant directly so that one usually has to work with approximations. M. Farber has carried out a certain number of computations with the aid of the lower bound given by the nilpotence of the kernel of the cup product. In this talk, I will introduce a new lower bound which is computable from a Sullivan model of the space and which is closer to the topological complexity than the cohomological one used by M. Farber.
© Lucile Vandembroucq.