26/04/2017, 14:15 — 15:15 — Sala P3.10, Pavilhão de Matemática
Lucile Vandembroucq, Universidade do Minho
Topological Complexity of the Klein Bottle
The notion of topological complexity of a space has been introduced by M. Farber in order to give a topological measure of the complexity of the motion planning problem in robotics. Surprisingly, the determination of this invariant for non-orientable surfaces has turned out to be difficult. A. Dranishnikov has recently established that the topological complexity of the non-orientable surfaces of genus at least 4 is maximal. In this talk, we will determine the topological complexity of the Klein bottle and extend Dranishnikov's result to all the non-orientable surfaces of genus at least 2. This is a work in collaboration with Daniel C. Cohen.