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Gottlieb Groups and Subgroups of the Group of Self-Homotopy Equivalences

김재룡|Nobuyuki Oda|Jianzhong Pan|우무하
대한수학회 (The Korean Mathematical Society)|2006.09|대한수학회지 (Journal of the KMS)|제43권 제5호|pp. 1047-1063

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Abstract

mathcal{E}(X) consisting of homotopy classes of self-homotopyequivalences that fix homotopy groups through the dimension of X andmathcal{E}_*(X) be the subgroup of mathcal{E} (X) that fix homologygroups for all dimension.In this paper, we establish some connections between the homotopy group of Xand the subgroup mathcal{E}_#(X)cap mathcal{E}_*(X) ofmathcal{E}(X).We also give some relations between pi_n (W),as well as a generalized Gottlieb group G_n^f(W,X),and a subset mathcal{M}{_{#}^f}_N (X, W) of [X, W]. Finally weestablish a connection between the coGottlieb group of X andthe subgroup of mathcal{E}(X) consisting of homotopy classes of self-homotopyequivalences that fix cohomology groups.

참고문헌 (14)

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