Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Topological complexity of the Klein bottle


Speaker: Daniel Cohen
Location: 2112 MSB
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).