Lusternik-Schnirelmann theory to Topological Complexity from A_∞-view point

2022/08/16 by Norio Iwase, Iwase, Norio
Computer Science · Mathematics · #55P05 #55P10 #55P45 #55P48 #55Q25 #55R35 #55R70 #55S10 #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 55M30 #Secondary 18M75 #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2208.07545

openalex publication_date 2022/08/16 · openalex created_date 2022/08/18 · openalex updated_date 2026/07/28

Abstract

We are trying to look over the Lusternik-Schnirelmann theory (L-S theory, for short) and the Topological Complexity (TC, for short) as a natural extension of the L-S theory. In particular, we focus on the impact of the ideas originated from E. Fadell and S. Husseini on both theories. More precisely, we see how their ideas on a category weight and a relative category drive the L-S theory and the TC.

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