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Verifying the Hilali conjecture up to formal dimension twenty

Journal of Homotopy and Related Structures volume 15, pages 323–331 (2020)Cite this article

Abstract

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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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics, Stony Brook University, New York, NY, 11794, USA

    Spencer Cattalani & Aleksandar Milivojević

Authors
  1. Spencer Cattalani
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  2. Aleksandar Milivojević
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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). https://doi.org/10.1007/s40062-020-00256-2

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  • DOI: https://doi.org/10.1007/s40062-020-00256-2

Keywords

  • Rational homotopy theory
  • Rationally elliptic spaces
  • Hilali conjecture