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On the Euler–Poincaré characteristics of a simply connected rationally elliptic CW-complex

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Abstract

For a simply connected rationally elliptic CW-complex X, we show that the cohomology and the homotopy Euler–Poincaré characteristics are related to two new numerical invariants namely \(\eta _{X}\) and \(\rho _{X}\) which we define using the Whitehead exact sequences of the Quillen and the Sullivan models of X.

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References

  1. Benkhalifa, M.: The group of self-homotopy equivalences of a rational space cannot be a free abelian group. J. Math. Soc. Jpn. (2022) (to appear)

  2. Benkhalifa, M.: The effect of cell-attachment on the group of self-equivalences of an elliptic space. Michigan Math. J. (2021). https://doi.org/10.1307/mmj/20195840

    Article  Google Scholar 

  3. Benkhalifa, M.: On the group of self-homotopy equivalences of an elliptic space. Proc. Am. Math. Soc. 148(6), 2695–2706 (2020)

    Article  MathSciNet  Google Scholar 

  4. Benkhalifa, M., Smith, S.B.: The effect of cell attachment on the group of self-equivalences of an \(R\)-local space. J. Homotopy Relat. Struct. 10(3), 549–564 (2015)

    Article  MathSciNet  Google Scholar 

  5. Benkhalifa, M.: Rational self-homotopy equivalences and Whitehead exact sequence. J. Homotopy Relat. Struct. 4(1), 135–144 (2009)

    MathSciNet  MATH  Google Scholar 

  6. Benkhalifa, M.: Whitehead exact sequence and differential graded free Lie algebra. Int. J. Math. 15(12), 1–19 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Félix, Y., Halperin, S., Thomas, J.-C.: Rational Homotopy Theory, Graduate Texts in Mathematics, vol. 205. Springer, New York (2001)

    Book  Google Scholar 

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Acknowledgements

The author is deeply grateful to the referee for a careful reading of the paper and valuable suggestions that greatly improved the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, University of Sharjah, Sharjah, United Arab Emirates

    Mahmoud Benkhalifa

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  1. Mahmoud Benkhalifa
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Correspondence to Mahmoud Benkhalifa.

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Communicated by Jonathan Rosenberg.

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Benkhalifa, M. On the Euler–Poincaré characteristics of a simply connected rationally elliptic CW-complex. J. Homotopy Relat. Struct. 17, 163–174 (2022). https://doi.org/10.1007/s40062-022-00301-2

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  • DOI: https://doi.org/10.1007/s40062-022-00301-2

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