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Topological complexity of the Klein bottleGeometry/Topology
|Start time:||Mon, Apr 24 2017, 1:10PM|
Topological complexity is a numerical homotopy-type invariant introduced by Farber about 15 years ago, motivated by the motion planning problem from robotics. For a space X, this invariant TC(X), the Schwarz genus of the fibration sending a path in X to its two endpoints, provides a measure of the complexity of navigation in X. Computing TC(X) is sometimes easy, sometimes hard. I will attempt to illustrate this, primarily with surfaces, including the Klein bottle, which is recent joint work with Lucile Vandembroucq (Univ. Minho).