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
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