Self-Closeness Number of Non-Simply-Connected Spaces

Yichen Tong

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arXiv · 2107.07109

Self-Closeness Number of Non-Simply-Connected Spaces

Yichen Tong

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Abstract

The self-closeness number $N\mathcal{E}(X)$ of a space $X$ is the least integer $k$ such that any self-map is a homotopy equivalence whenever it is an isomorphism in the $n$-th homotopy group for each $n\le k$. We discuss the self-closeness numbers of certain non-simply-connected $X$ in this paper. As a result, we give conditions for $X$ such that $N\mathcal{E}(X)=N\mathcal{E}(\widetilde{X})$, where $\widetilde{X}$ is the universal covering space of $X$.

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Yichen Tong. 2021-07-15. Self-Closeness Number of Non-Simply-Connected Spaces. https://arxiv.org/abs/2107.07109

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