Rational cohomology of classifying spaces and Hilali conjecture

Abdelhadi Zaim

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; πi(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.

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Published: 2022-03-21

How to Cite this Article:

Abdelhadi Zaim, Rational cohomology of classifying spaces and Hilali conjecture, J. Math. Comput. Sci., 12 (2022), Article ID 114

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.

 

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