On the sequential topological complexity of group homomorphisms

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 prove that the sequential topological complexity of any nonzero homomorphism of a torsion group cannot be finite. Also, we give the characterisation of cohomological dimension of group homomorphisms.