S. Mescher (U. Halle-Wittenberg), Sequential topological complexities and sectional categories of subgroup inclusions

The sequential topological complexities (TCs) of a space are integer-valued homotopy invariants that are motivated by the motion planning problem from robotics and express the complexity of motion planning if the robots are supposed to make predetermined intermediate stops along their ways. After outlining their definitions, I will discuss the sequential TCs of aspherical spaces and describe how they can be investigated by purely algebraic means. The study of sectional categories of subgroup inclusions is a straightforward generalization of this algebraic setting and we will discuss how to obtain lower bounds on their values using elementary homological algebra. Afterwards, we will discuss consequences for sequential TCs and for the parametrized topological complexity of epimorphisms. This is joint work with Arturo Espinosa Baro, Michael Farber and John Oprea.