# Generalized relative Hilali conjecture

Volume 29, Issue 4, pp 399--406
Publication Date: November 24, 2022 Submission Date: April 13, 2022 Revision Date: May 17, 2022 Accteptance Date: August 30, 2022
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### Authors

A. Zaim - Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, University Hassan II, Casablanca, Morocco.

### Abstract

Let $F{}^{\underrightarrow{j}}E{}^{\underrightarrow{p}}B$ be a fibration of simply connected elliptic CW-complexes. Motivated by the famous Hilali conjecture, Yamaguchi and Yokura \cite{8} proposed a relative version of Hilali conjecture which speculates that $\mbox{dim ker }(\pi_{\ast}(p)\otimes{\mathbb{Q}})\leq\mbox{dim ker }H_{\ast}(p;\mathbb{Q})+1.$ Our purpose in this paper is to generalize the relative Hilali conjecture. Therefore, we suggest $\mbox{dim ker }( \pi_{\ast}\left(j\right)\otimes{\mathbb{Q}}) + \mbox{dim ker } (\pi_{\ast}\left( p\right)\otimes{\mathbb{Q}}) \leq \mbox{dim ker } H_{\ast}\left( j;\mathbb{Q}\right) + \mbox{dim ker } H_{\ast}\left( p;\mathbb{Q}\right) + 1.$ It includes the Hilali conjecture and Yamaguchi-Yokura conjecture as special cases. Furthermore, we prove this conjecture for non trivial cases.

### Share and Cite

##### ISRP Style

A. Zaim, Generalized relative Hilali conjecture, Journal of Mathematics and Computer Science, 29 (2023), no. 4, 399--406

##### AMA Style

Zaim A., Generalized relative Hilali conjecture. J Math Comput SCI-JM. (2023); 29(4):399--406

##### Chicago/Turabian Style

Zaim, A.. "Generalized relative Hilali conjecture." Journal of Mathematics and Computer Science, 29, no. 4 (2023): 399--406

### Keywords

• Rational homotopy theory
• Sullivan models
• elliptic space
• relative Hilali conjecture
• rational cohomology

•  55P62
•  55Q52
•  55Q40