Self-homotopy equivalences of Moore spaces depending on cohomotopy groups
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초록
Given a topological space $X$ and a non-negative integer $k$, $\E_{k}^{\sharp}(X)$ 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 $\E(X)$. We find certain homotopic tools for computations of $\E_{k}^{\sharp}(X)$. Using these results, we determine $\E_{k}^{\sharp}(M(G,n))$ for $k\geq n$, where $M(G, n)$ is a Moore space type of $(G, n)$ for a finitely generated abelian group $G$.
Abstract
Given a topological space $X$ and a non-negative integer $k$, $\E_{k}^{\sharp}(X)$ 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 $\E(X)$. We find certain homotopic tools for computations of $\E_{k}^{\sharp}(X)$. Using these results, we determine $\E_{k}^{\sharp}(M(G,n))$ for $k\geq n$, where $M(G, n)$ is a Moore space type of $(G, n)$ for a finitely generated abelian group $G$.
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