Rational cohomology of classifying spaces and Hilali conjecture

Zaim, Abdelhadi

doi:10.28919/jmcs/7238

J. Math. Comput. Sci. 12 (2022), Article ID 114

Rational cohomology of classifying spaces and Hilali conjecture

Abdelhadi Zaim

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Abstract

Let X be a simply connected space with finite-dimensional rational homotopy groups. Denote by Bau₁(X) the classifying space of fibrations with fiber X and max π_∗(X)=max {i; π_i(X)≠0}. In this paper, we show that the dimensional rational cohomology and the Lusternik-Schnirelmann category of Bau₁(X) are infinite if max π_∗(X) is odd. Our results apply, in particular, when X is elliptic. As a consequence, we prove the Hilali conjecture for classifying space.

Published: 21 March 2022
Volume: 12 (2022)
License: CC BY 3.0

Copyright © 2022 Abdelhadi Zaim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

A. Zaim, Rational cohomology of classifying spaces and Hilali conjecture, J. Math. Comput. Sci. 12 (2022), 114. https://doi.org/10.28919/jmcs/7238

BibTeX

@article{Zaim2022,
  author  = {Zaim, Abdelhadi},
  title   = {Rational cohomology of classifying spaces and Hilali conjecture},
  journal = {J. Math. Comput. Sci.},
  volume  = {12},
  year    = {2022},
  pages   = {114},
  doi     = {10.28919/jmcs/7238}
}