Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
12 December 2019 |
27 December 2019 |
10 March 2020 |
Abstract: The well-known Hilali conjecture is one claiming that if $X$ is a simplyconnected elliptic space, then dim $\pi_{\ast}\left( X,%%TCIMACRO{\U{211a} }%%BeginExpansion\mathbb{Q}%EndExpansion\right) \leq$ dim $H_{\ast}(X;Q)$. In this talk we propose that if$f:X\rightarrow Y$ is a continuous map of simply connected elliptic spaces,then dim Ker $\pi_{\ast}\left( f;%%TCIMACRO{\U{211a} }%%BeginExpansion\mathbb{Q}%EndExpansion\right) \leq$ dim Ker $H_{\ast}(f;Q)+1$, and we prove this for certainreasonable cases. Our proposal is a relative version of the Hilali conjectureand it includes the Hilali conjecture as a special case.
