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Gaps in the Milnor–Moore spectral sequence and the Hilali conjecture

  • Youssef RamiEmail author
Article

Abstract

Let X be a simply-connected space, \((\Lambda V, d)\) its minimal Sullivan model and \(d_k\) (\(k\ge 2\)) the first non-zero homogeneous part of the differential d. In this paper, assuming that \((\Lambda V, d_k)\) is elliptic, we show that \(H(\Lambda V,d)\) has no \(e_0\)-gap and consequently we confirm the Hilali conjecture when \(V = V^{odd}\) or else when \(k\ge 3\).

Keywords

Milnor-Moore spectral sequence Hilali conjecture Sullivan models Elliptic spaces 

Résumé

Soit X un espace topologique simplement connexe, \((\Lambda V, d)\) son modéle minimal de Sullivan et \(d_k\) (\(k\ge 2\)) la premiére partie homogéne non nulle de la différentielle d. Dans cet article, en supposant que \((\Lambda V, d_k)\) est elliptique, nous montrons que \(H(\Lambda V,d)\) n’a aucun \(e_0\)-écart et par conséquent, nous confirmons la conjecture de Hilali lorsque \(V = V^{impair}\) ou lorsque \(k\ge 3\)

Mathematics Subject Classification

55P62 55T99 55Q15 

Notes

Acknowledgements

I would like to thank the referee for his valuable remarks and suggestions. I am also grateful to all members of the Moroccan Area of Algebraic Topology group for several discussions that contributed to the achievement of my results.

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Copyright information

© Fondation Carl-Herz and Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université Moulay Ismail, Faculté des SciencesMeknésMorocco

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