Abstract
The Hilali conjecture claims that a simply connected rationally elliptic space $X$ satisfies the inequality $\dim (\pi_*(X)\otimes \mathbb{Q} ) \leqq \dim H_*(X;\mathbb{Q} )$. In this paper we show that for any such space $X$ there exists a positive integer $n_0$ such that for any $n \geqq n_0$ the strict inequality $\dim (\pi_*(X^n)\otimes \mathbb{Q} ) \lt \dim H_*(X^n; \mathbb{Q} )$ holds, where $X^{n}$ is the product of $n$ copies of $X$.
Funding Statement
This work is supported by JSPS KAKENHI Grant Numbers JP16H03936 and JP19K03468.
Acknowledgment
The author would like to thank Toshihiro Yamaguchi for useful comments.
Citation
Shoji Yokura. "The Hilali conjecture on product of spaces." Tbilisi Math. J. 12 (4) 123 - 129, October 2019. https://doi.org/10.32513/tbilisi/1578020572
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