## African Diaspora Journal of Mathematics

### On a Relative Hilali Conjecture

#### Abstract

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

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

Dates
First available in Project Euclid: 6 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1530842661

Mathematical Reviews number (MathSciNet)
MR3824427

Zentralblatt MATH identifier
07002177

Subjects
Primary: 55P62: Rational homotopy theory

#### Citation

Yamaguchi, Toshihiro; Yokura, Shoji. On a Relative Hilali Conjecture. Afr. Diaspora J. Math. (N.S.) 21 (2018), no. 1, 81--86. https://projecteuclid.org/euclid.adjm/1530842661