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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 29, Issue 2


A note on the Hilali conjecture

Manuel Amann
  • Corresponding author
  • Fakultät für Mathematik, Institut für Algebra und Geometrie, Karlsruher Institut für Technologie, Englerstraße 2, 76131 Karlsruhe, Germany
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Published Online: 2016-05-21 | DOI: https://doi.org/10.1515/forum-2015-0078


In this short note we observe that the Hilali conjecture holds for 2-stage spaces, i.e. we argue that the dimension of the rational cohomology is at least as large as the dimension of the rational homotopy groups for these spaces. We also prove the Hilali conjecture for a class of spaces which puts it into the context of fibrations.

Keywords: Hilali conjecture; rational cohomology groups; rational homotopy groups

MSC 2010: 55Q52; 55P62


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About the article

Received: 2015-04-27

Revised: 2016-02-02

Published Online: 2016-05-21

Published in Print: 2017-03-01

Citation Information: Forum Mathematicum, Volume 29, Issue 2, Pages 251–257, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0078.

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