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October 2019 The Hilali conjecture on product of spaces
Shoji Yokura
Tbilisi Math. J. 12(4): 123-129 (October 2019). DOI: 10.32513/tbilisi/1578020572

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

Download 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

Information

Received: 29 September 2019; Accepted: 25 October 2019; Published: October 2019
First available in Project Euclid: 3 January 2020

zbMATH: 07179176
MathSciNet: MR4047580
Digital Object Identifier: 10.32513/tbilisi/1578020572

Subjects:
Primary: 55P62
Secondary: 55N99, 55Q40

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences

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Vol.12 • No. 4 • October 2019
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