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Verifying the Hilali conjecture up to formal dimension twenty


We prove that in formal dimension \(\le 20\) the Hilali conjecture holds, i.e. that the total dimension of the rational homology bounds from above the total dimension of the rational homotopy for a simply connected rationally elliptic space.

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The authors would like to acknowledge the support of the Directed Reading Program at Stony Brook University, under which this project was initiated. Several computations were carried out with the Commutative Differential Graded Algebras module for SageMath [8] written by Miguel Marco and John Palmieri, for which the authors are duly grateful. We thank the referee for their help in streamlining the exposition.

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Correspondence to Spencer Cattalani.

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Communicated by Scott Wilson.

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Cattalani, S., Milivojević, A. Verifying the Hilali conjecture up to formal dimension twenty. J. Homotopy Relat. Struct. 15, 323–331 (2020).

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  • Rational homotopy theory
  • Rationally elliptic spaces
  • Hilali conjecture