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

Authors

  • K. Boutahir Department of Mathematics, My Ismail University, B.P. 11201 Zitoune, Meknès, Morocco
  • A. El Houari Department of Mathematics, My Ismail University, B.P. 11201 Zitoune, Meknès, Morocco
  • Y. Rami Department of Mathematics, My Ismail University, B.P. 11201 Zitoune, Meknès, Morocco

DOI:

https://doi.org/10.17398/

Keywords:

(Higher) Topological complexity, Hopf invariant, Zero-divisor-cup-length, spherical cohomology class

Abstract

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.

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References

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Published

2026-03-26

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How to Cite

Rationality conjecture for finite CW-complexes with unique spherical cohomology class and high-torsion lens spaces. (2026). Extracta Mathematicae, 16 pp. https://doi.org/10.17398/