Rationality conjecture for finite CW-complexes with unique spherical cohomology class and high-torsion lens spaces

• K. Boutahir ; A. El Houari ^[1] ; Y. Rami
  1. [1] Department of Mathematics, My Ismail University, B.P. 11201 Zitoune, Meknès, Morocco
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 41, Nº 1, 2026, págs. 143-157
• Idioma: inglés
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• Resumen

  • This paper examines the weak Rationality Conjecture for (r −1)-connected CW-complexes X admitting a unique spherical cohomology class u ∈ Hr (X, Z) for some r ≥ 2. We affirm this conjecture for such complexes of dimension kr where uk ̸= 0. We provide a non-exhaustive list of finite CW-complexes satisfying the conjecture. Furthermore, we investigate some high-torsion Lens spaces Lm2n+1, which are defined as orbit spaces S2n+1 /Zm . The generating functions of these lens spaces confirm both the Weak and Strong Rationality Conjectures under certain conditions.