논문KCI 등재
On the Characterization of $F_{0}$-spaces
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Let $X$ be a simply connected rationally elliptic space such that $H^{2}(X; \Q)\neq0$. In this paper, we show that if $ H^{2n}(X^{[2n-2]}; \Q)=0$ or if $\pi_{2n}(X^{2n}) \otimes \Q=0$ for all $n$, then $X$ is an $F_{0}$-space.
Abstract
Let $X$ be a simply connected rationally elliptic space such that $H^{2}(X; \Q)\neq0$. In this paper, we show that if $ H^{2n}(X^{[2n-2]}; \Q)=0$ or if $\pi_{2n}(X^{2n}) \otimes \Q=0$ for all $n$, then $X$ is an $F_{0}$-space.
참고문헌 (8)
- M. Benkhalifa, "Postnikov decomposition and the group of self-equivalences of a rationalized space", Homology Homotopy Appl, 19(1), pp.209~224 (2017)[DOI]
- M. Benkhalifa, "On the group of self-homotopy equivalences of an elliptic space", Proc. Amer. Math. Soc, 148(6), pp.2695~2706 (2020)[DOI]
- M. Benkhalifa, "On the Euler-Poincar´e characteristics of a simply connected rationally elliptic CW-complex", J. Homotopy Relat. Struct, 17(2), pp.163~174 (2022)[DOI]
- M. Benkhalifa, "On the group of self-homotopy equivalences of an almost formal space", Quaestiones Mathematicae (2022)[DOI]
- M. Benkhalifa, "The effect of cell-attachment on the group of self-equivalences of an elliptic space", Michigan Math. J, 71(2), pp.611~617 (2022)
- M. Benkhalifa, "The group of self-homotopy equivalences of a rational space cannot be a free abelian group", J. Math. Soc. Japan[DOI]
- M. Benkhalifa, "The effect of cell-attachment on the group of selfequivalences of an R-localized space", J. Homotopy Relat. Struct, 10(3), pp.549~564 (2015)[DOI]
- Y. F´elix, "Rational homotopy theory, Graduate Texts in Mathematics, 205" (2001), Springer-Verlag
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