Topological complexity and the homotopy cofibre of the diagonal map

2011/06/24 by J.M. García-Calcines, Calcines, J., Lucile Vandembroucq +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Algebraic Topology (math.AT) #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Sphingolipid Metabolism and Signaling

paper · pdf · doi:10.48550/arxiv.1106.4943

openalex publication_date 2011/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we analyze some relationships between the topological complexity of a space X and the category of C_ΔX, the homotopy cofibre of the diagonal map Δ_X:X→ X× X. We establish the equality of the two invariants for several classes of spaces including the spheres, the H-spaces, the real and complex projective spaces and almost all the (standard) lens spaces.

Citations

• The sectional category of a map

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