On the rationality conjecture of some finite CW-complexes

Abstract

In this paper, we establish the rationality conjecture raised in \cite{FKS} for any $(r-1)$-connected ($r\ge 2$) $kr$-dimensional CW-complex $X$ ($k\ge 2$) having a unique spherical cohomology class $u\in {\tilde{H}}^r(X,\mathbb{Z})$ such that $u^k\ne 0$. %which is nilpotent with order of nilpotency equal to $k+1$. Next, we illustrate (topologically) our result by giving the minimal cell structure of such a CW-complex whose cohomology is a truncated polynomial algebra.

12 pages