Sequential topological complexities and sectional categories of subgroup inclusions |
Stephan Mescher (Uni Halle) |
Donnerstag, 12. Dezember 2024 10:00Uhr |
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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 in the first part of my talk and describe how they can be investigated by purely algebraic means. We will also take a look at a generalization of this algebraic setting, namely sectional categories of subgroup inclusions. In the second part of my talk, I will present a general lower bound on their values and derive consequences for sequential TCs and parametrized topological complexities of epimorphisms. We will investigate the methodology of the proof of this lower bound, in which all key steps are carried out using elementary homological algebra. This is joint work with Arturo Espinosa Baro, Michael Farber and John Oprea. |