대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권2호
  • /
  • Pages.643-648
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  • 2023
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON THE CHARACTERIZATION OF F0-SPACES

  • Mahmoud Benkhalifa (Department of Mathematics Faculty of Sciences University of Sharjah)
  • 투고 : 2022.06.15
  • 심사 : 2022.09.21
  • 발행 : 2023.04.30
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초록

Let X be a simply connected rationally elliptic space such that H2(X; ℚ) ≠ 0. In this paper, we show that if H2n(X[2n-2]; ℚ) = 0 or if π2n(X2n) ⊗ ℚ = 0 for all n, then X is an F0-space.

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과제정보

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

참고문헌

  1. M. Benkhalifa, Postnikov decomposition and the group of self-equivalences of a rationalized space, Homology Homotopy Appl. 19 (2017), no. 1, 209-224. https://doi.org/10.4310/HHA.2017.v19.n1.a11 
  2. M. Benkhalifa, On the group of self-homotopy equivalences of an elliptic space, Proc. Amer. Math. Soc. 148 (2020), no. 6, 2695-2706. https://doi.org/10.1090/proc/14900 
  3. M. Benkhalifa, On the Euler-Poincar'e characteristics of a simply connected rationally elliptic CW-complex, J. Homotopy Relat. Struct. 17 (2022), no. 2, 163-174. https://doi.org/10.1007/s40062-022-00301-2 
  4. M. Benkhalifa, On the group of self-homotopy equivalences of an almost formal space, Quaestiones Mathematicae (2022). https://doi.org/10.2989/16073606.2022.2044405 
  5. M. Benkhalifa, The effect of cell-attachment on the group of self-equivalences of an elliptic space, Michigan Math. J. 71 (2022), no. 2, 611-617. 
  6. M. Benkhalifa, The group of self-homotopy equivalences of a rational space cannot be a free abelian group, J. Math. Soc. Japan. https://doi.org/10.2969/jmsj/87158715 
  7. M. Benkhalifa and S. B. Smith, The effect of cell-attachment on the group of self-equivalences of an R-localized space, J. Homotopy Relat. Struct. 10 (2015), no. 3, 549-564. https://doi.org/10.1007/s40062-014-0076-5 
  8. Y. F'elix, S. Halperin, and J.-C. Thomas, Rational homotopy theory, Graduate Texts in Mathematics, 205, Springer-Verlag, New York, 2001. https://doi.org/10.1007/978-1-4613-0105-9