## African Diaspora Journal of Mathematics

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

### On a Relative Hilali Conjecture

Toshihiro Yamaguchi and Shoji Yokura

#### 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

**Keywords**

Betti number elliptic space Sullivan minimal model

#### 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