GOTTLIEB GROUPS AND SUBGROUPS OF THE GROUP OF SELF-HOMOTOPY EQUIVALENCES

Title & Authors
GOTTLIEB GROUPS AND SUBGROUPS OF THE GROUP OF SELF-HOMOTOPY EQUIVALENCES
Kim, Jae-Ryong; Oda, Nobuyuki; Pan, Jianzhong; Woo, Moo-Ha;

Abstract
Let $\small{\varepsilon_#(X)}$ be the subgroups of $\small{\varepsilon(X)}$ consisting of homotopy classes of self-homotopy equivalences that fix homotopy groups through the dimension of X and $\small{\varepsilon_*(X) }$ be the subgroup of $\small{\varepsilon(X)}$ that fix homology groups for all dimension. In this paper, we establish some connections between the homotopy group of X and the subgroup $\small{\varepsilon_#(X)\cap\varepsilon_*(X)\;of\;\varepsilon(X)}$. We also give some relations between $\small{\pi_n(W)}$, as well as a generalized Gottlieb group $\small{G_n^f(W,X)}$, and a subset $\small{M_{#N}^f(X,W)}$ of [X, W]. Finally we establish a connection between the coGottlieb group of X and the subgroup of $\small{\varepsilon(X)}$ consisting of homotopy classes of self-homotopy equivalences that fix cohomology groups.
Keywords
self-homotopy equivalences;Gottlieb groups;coGottlieb groups;
Language
English
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