# Exposé par Éric Goubault: «Directed topological complexity»

**Speaker:**Éric Goubault

**Location:**Salle Philippe Flajolet, LIX

**Date:**Mon, 1 Jul 2019, 11:00-12:00

Pour le prochain séminaire de l'équipe Cosynus, nous aurons le plaisir d'accueillir Éric Goubault qui nous parlera de complexité topologique dirigée.

**Résumé:** *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 {F _{1},…,F_{n},…} of the set of reachable states of some directed space X, such that there is a continuous section from each of the F_{i} to the space of directed paths which is right inverse to the end points map. The size of this partition measures the minimal complexity that a motion planning algorithm should have, for controlling such a system. Also, 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, a number of higher-dimensional spaces and in particular, directed spheres. This is ongoing work with Aurélien Sagnier and Michael Farber.*