African Diaspora Journal of Mathematics

On a Relative Hilali Conjecture

Toshihiro Yamaguchi and Shoji Yokura

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The well-known Hilali conjecture stated in [9] is one claiming that if $X$ is a simply connected elliptic space, then $ \dim \pi_*(X)\otimes {\mathbb Q} \leq \dim H_*(X; {\mathbb Q})$. In this paper we propose that if $f:X \to Y$ is a continuous map of simply connected elliptic spaces, then $\dim {\rm Ker} \ \pi_*(f)_{\mathbb Q}\leq \dim {\rm Ker}\ H_*(f; {\mathbb Q})+1$, and we prove this for certain reasonable cases. Our proposal is a relative version of the Hilali conjecture and it includes the Hilali conjecture as a special case.

Article information

Afr. Diaspora J. Math. (N.S.), Volume 21, Number 1 (2018), 81-86.

First available in Project Euclid: 6 July 2018

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P62: Rational homotopy theory

Betti number elliptic space Sullivan minimal model


Yamaguchi, Toshihiro; Yokura, Shoji. On a Relative Hilali Conjecture. Afr. Diaspora J. Math. (N.S.) 21 (2018), no. 1, 81--86.

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