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 Self-homotopy equivalences of Moore spaces depending on cohomotopy groups J. Korean Math. Soc.Published online 2019 Apr 10 Ho Won Choi, Kee Young Lee, and Hyung Seok Oh Korea University Abstract : Given a topological space $X$ and a non-negative integer $k$, \mathcal{E}_k^{\sharp} (X) is the set of all self-homotopy equivalences of $X$ that do not change maps from $X$ to an $t$-sphere $S^t$ homotopically by the composition for all $t \geq  k$. This set is a subgroup of the self-homotopy equivalence group $\mathcal{E}(X)$. We find certain homotopic tools for computations of $\mathcal{E}_k^{\sharp} (X)$. Using these results, we determine $\mathcal{E}_k^{\sharp} (M(G; n))$ for $k\geq  n$, where $M(G; n)$ is a Moore space type of $(G; n)$ for a finitely generated abelian group $G$. Keywords : Self-homotopy equivalence, Cohomotopy group, Moore space, co-Moore space MSC numbers : 55P10, 55Q05, 55Q55 Full-Text :