Lower Multiplicity Bounds via Classifying Spaces

Explore variations of the Lusternik--Schnirelmann category in this lecture, focusing on open covers with constraints on the fundamental group level. Learn how LS-category invariants can be analyzed through equivariant methods, particularly using classifying spaces for families of subgroups to obtain lower bounds. Delve into the application of these methods in the case of the family of amenable subgroups. Gain insights into advanced topics in algebraic topology and their applications in studying topological spaces.