On the higher rational topological complexity of certain elliptic spaces

2025/03/22 by Said Hamoun, Hamoun, Said
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2503.17595

openalex publication_date 2025/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Through this paper, we show that TC_r(Z)≤ r⋅ cat(Z)+χ_π(Z), for any simply-connected elliptic space Z admitting a pure minimal Sullivan model with a differential of constant length. Here χ_π(Z) denotes the homotopy characteristic and r is an integer greater or equals than 2. We also give a lower bound for TC_r in the framework of coformal spaces and we compute the exact value of TC_r for certain families of spaces.

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