Alexander Dranishnikov - On the LS-Category of Group Homomorphisms

Explore the concept of Lusternik-Schnirelmann category for group homomorphisms in this 46-minute lecture by Alexander Dranishnikov. Delve into the historical context of Eilenberg and Ganea's 1950s proof equating the LS-category of a discrete group with its cohomological dimension. Examine the possibility of extending this equality to group homomorphisms, specifically investigating the relationship between cat(φ) and cd(φ) for a homomorphism φ : Γ → Λ. Learn about proven cases for certain classes of groups and discover a counterexample involving geometrically finite groups. Gain insights into advanced topics in algebraic topology and group theory through this in-depth presentation from the Applied Algebraic Topology Network.