Journal of Homotopy and Related Structures

, Volume 11, Issue 3, pp 493–501 | Cite as

On Hilali’s conjecture related to Halperin’s

  • Badr Ben El Krafi
  • Mohamed Rachid Hilali
  • My Ismail Mamouni
Article
  • 66 Downloads

Abstract

In this paper, we focus on Hilali’s conjecture that, for any simply-connected elliptic CW-complex X, the total sum of the rational Betti numbers is at least as large as the total rank of its rational homotopy. We investigate this conjecture for coformal spaces and suggest some research directions to resolve it completely. Finally, we put up a bridge between the Hilali conjecture and that of Halperin: the toral rank conjecture and use it to establish the latter holds for all manifolds of dimension less than 16 and whose toral rank is equal to 4.

Keywords

Rational homotopy theory Minimal models Coformal spaces  Toral rank conjecture 

Mathematics Subject Classification

Primary 55P62  Secondary 55T05 

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Copyright information

© Tbilisi Centre for Mathematical Sciences 2015

Authors and Affiliations

  • Badr Ben El Krafi
    • 1
  • Mohamed Rachid Hilali
    • 1
  • My Ismail Mamouni
    • 2
  1. 1.Département de Mathématiques et d’InformatiqueFaculté des Sciences Ain ChockCasablancaMorocco
  2. 2.Centre de Préparation à l’Agrégation, CRMEF RabatRabatMorocco

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