On the Topological Complexity of Maps

2020/11/20 by Jamie Scott, Scott, Jamie · 5 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Glycosylation and Glycoproteins Research #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2011.10646

openalex publication_date 2020/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and develop a homotopy invariant notion for the topological complexity of a map f:X → Y, denoted TC(f), that interacts with TC(X) and TC(Y) in the same way cat(f) interacts with cat(X) and cat(Y). Furthermore, TC(f) and cat(f) satisfy the same inequalities as TC(X) and cat(X). We compare it to other invariants defined in the papers [15,16,17,18,20]. We apply TC(f) to studying group homomorphisms f:H→ G.

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