Next Talks


  • Date: May 3, 2019
  • Speaker: Eric Goubault

Title: Directed topological complexity

Abstract:

I will introduce in this talk a variant of topological complexity, that can be applied to help classify directed spaces, and has applications to the study of dynamical systems in the large, such as differential inclusions. Directed topological complexity looks for specific partitions {F1,…,Fn,…} of the set of reachable states of some directed space X, such that there is a continuous section from each of the Fi to the space of directed paths which is right inverse to the end points map. As in the classical case, this sheds an interesting light on a number of directed invariants, and we discuss in particular dicontractibility. We will also show some examples of calculations on directed graphs, non-positively curved cubical complexes, and directed spheres.
This ongoing work with Aurélien Sagnier and Michael Farber.

Keywords:

directed algebraic topology, topological complexity, directed invariants, homotopy theory, differential inclusions, control theory




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