On the sequential topological complexity of group homomorphisms

2024/02/20 by Nursultan Kuanyshov, Kuanyshov, Nursultan · 3 citations
Computer Science · Mathematics · #20K10 #20K30 #20K45 #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Primary 50M30 #Rings, Modules, and Algebras #Secondary 20J06

paper · pdf · doi:10.48550/arxiv.2402.13389

openalex publication_date 2024/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and develop a homotopy invariant notion for the sequential topological complexity of a map f:X→ Y, denoted TC_r(f), that interacts with TC_r(X) and TC_r(Y) in the same way Jamie Scott's topological complexity map TC(f) interacts with TC(X) and TC(Y). Furthermore, we apply TC_r(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.

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