Relative category and monoidal topological complexity

2014/03/31 by José Gabriel Carrasquel-Vera, Carrasquel-Vera, J. G., J.M. García-Calcines +3 · 1 citation
Mathematics · #55M30 #55P62 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1403.8089

openalex publication_date 2014/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If a map f has a homotopy retraction, then Doeraene and El Haouari conjectured that the sectional category and the relative category of f are the same. In this work we discuss this conjecture for some lower bounds of these invariants. In particular, when we consider the diagonal map, we obtain results supporting Iwase-Sakai's conjecture which asserts that the topological complexity is the monoidal topological complexity.

Citations

• On category, in the sense of Lusternik-Schnirelmann

Cited by

• Parametrized topological complexity of bundles of real projective spaces, I

Related

• Generalized topological complexity and its monoidal version
• Up to one approximations of sectional category and topological complexity
• Relative sectional category revisited
• On topological complexity and LS-category
• Topological complexity and the homotopy cofibre of the diagonal map