Abstract: Topological complexity of a (phase) space X is a rough, but rigorous lower bound on the complexity of motion planning in X. It is an integer which depends only on the homeomorphism type of X and is a relative of Lusternik-Snirelman category.
In the last decade, quite a few (homological) methods have been developed to get upper and lower bounds on this invariant, but it is in general not easy to calculate.
In the talk, we take up a method of Grant and Mescher, who computed the topological complexity of symplectic manifolds whose symplectic class is atoroidal using analytical methods. We provide a purely topological proof of their result, which then covers a wider class of spaces. Before we get to the result, which has been obtained jointly with Luca Sandrock, we give a short introduction to the concept of "topological complexity" and its main features.
