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Explore a 49-minute mathematics lecture from the Applied Algebraic Topology Network that introduces a homotopy-invariant concept of sequential topological complexity for map functions f:X→Y, denoted as TC_{r}(f). Learn how this notion relates to TC_{r}(X) and TC_{r}(Y) in parallel with Jamie Scott's topological complexity map TC(f) and its relationship to TC(X) and TC(Y). Discover applications to group homomorphisms ϕ:Γ→Λ through detailed computations involving various group types including free groups, surface groups, abelian groups, nilpotent groups, and almost nilpotent groups. Examine the characterization of cohomological dimension in group homomorphisms and engage with current open problems in the field.
