Maps of degree one, relative LS category and higher topological complexities

2020/11/27 by Yuli B. Rudyak, Soumen Sarkar, Rudyak, Yuli B. +1
Computer Science · Mathematics · #55M30 #55S40 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2011.13531

openalex publication_date 2020/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce relative LS category of a map and study some of its properties. Then we introduce `higher topological complexity' of a map, a homotopy invariant. We give a cohomological lower bound and compare it with previously known `topological complexity' of a map. Moreover, we study the relation between Lusternik-Schnirelmann category and topological complexity of two closed oriented manifolds connected by a degree one map.

Citations

• On category, in the sense of Lusternik-Schnirelmann
• Higher equivariant and invariant topological complexity

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• Homotopic distance between maps
• On LS-category and topological complexity of connected sum
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