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

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.