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This paper observes that the induced homomorphisms on cohomology
groups by a cyclic map are trivial. For a CW-complex $X$, we use
the fact to obtain some conditions of $X$ so that the $n$-th
Gottlieb group $G_{n}(X)$ is trivial for an even positive integer
$n$. As corollaries, for any positive integer $m$, we obtain
$G_{2m}(S^{2m})=0$ and $G_2(CP^m)=0$ which are due to D. H.
Gottlieb and G. Lang respectively, where $S^{2m}$ is the $2m$-
dimensional sphere and $CP^m$ is the complex projective $m$-space.
Moreover, we show that $G_4(HP^m)=0$ and $G_8(\Pi)=0$, where
$HP^m$ is the quaternionic projective $m$-space for any positive
integer $m$ and $\Pi$ is the Cayley projective space.
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참고문헌 (10)
참고문헌 신청
/ 1969 / {\it Evaluation subgroups of homotopy groups} : 729 ~
/ 1972 / {\it Evaluation subgroups of factor spaces} : 701 ~
/ 1989 / Homotopy theorey
/ 1990 / Concise tables of James numbers and some homotopy classical Lie groups and associated homogeneous spaces
/ 1993 / The G-sequence and the omega-homology of a CW-pair : 221 ~
/ 1972 / {\it Evaluation subgroups of factor spaces} : 701 ~
/ 1989 / Homotopy theorey
/ 1990 / Concise tables of James numbers and some homotopy classical Lie groups and associated homogeneous spaces
/ 1993 / The G-sequence and the omega-homology of a CW-pair : 221 ~
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