Abstract
We define and develop a homotopy invariant notion for the sequential topological complexity of a map f:X→Y, denoted TCr(f), that interacts with TCr(X) and TCr(Y) in the same way Jamie Scott's topological complexity map TC(f) interacts with TC(X) and TC(Y). Furthermore, we apply TCr(f) to studying group homomorphisms ϕ:Γ→Λ.In addition, we give the characterization of cohomological dimension of group homomorphisms.
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