On topological complexity and LS-category

2012/07/31 by Alexander Dranishnikov, Dranishnikov, Alexander
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1207.7309

openalex publication_date 2012/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present some results supporting the Iwase-Sakai conjecture about coincidence of the topological complexity TC(X) and monoidal topological complexity TC^M(X). Using these results we provide lower and upper bounds for the topological complexity of the wedge X\vee Y. We use these bounds to give a counterexample to the conjecture asserting that TC(X')≤ TC(X) for any covering map p:X'→ X. We discuss a possible reduction of the monoidal topological complexity to the LS-category. Also we apply the LS-category to give a short proof of the Arnold-Kuiper theorem.

Related

• Relative category and monoidal topological complexity
• Topological Complexity of wedges
• Generalized topological complexity and its monoidal version
• Relative LS categories and higher topological complexities of maps
• Discrete Topological complexity