Generalized relative Hilali conjecture
Volume 29, Issue 4, pp 399--406
https://doi.org/10.22436/jmcs.029.04.08
Publication Date: November 24, 2022
Submission Date: April 13, 2022
Revision Date: May 17, 2022
Accteptance Date: August 30, 2022
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
MSC
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