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2018 On a Relative Hilali Conjecture
Toshihiro Yamaguchi, Shoji Yokura
Afr. Diaspora J. Math. (N.S.) 21(1): 81-86 (2018).

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.

Citation

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Toshihiro Yamaguchi. Shoji Yokura. "On a Relative Hilali Conjecture." Afr. Diaspora J. Math. (N.S.) 21 (1) 81 - 86, 2018.

Information

Published: 2018
First available in Project Euclid: 6 July 2018

zbMATH: 07002177
MathSciNet: MR3824427

Subjects:
Primary: 55P62

Rights: Copyright © 2018 Mathematical Research Publishers

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Vol.21 • No. 1 • 2018
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