Homotopy classification of based maps between $\mathbf{A}_n^2$-complexes
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866911768450695168 |
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| author | Li, Pengcheng |
| author_facet | Li, Pengcheng |
| contents | Let $X,Y$ be $(n-1)$-connected finite pointed CW-complexes of dimension at most $n+2$, $n\geq 3$. In this paper we give elementary proofs of the abelian group structure of $[X,Y]$ of homotopy classes of based maps from $X$ to $Y$, which was due to Baues and Schmidt. Furthermore, we determine the explicit generators associated to $[X,Y]$. As an application, we compute certain (sub)groups of self-homotopy equivalences of certain Chang complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_03049 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Homotopy classification of based maps between $\mathbf{A}_n^2$-complexes Li, Pengcheng Algebraic Topology 55Q05, 55P10 Let $X,Y$ be $(n-1)$-connected finite pointed CW-complexes of dimension at most $n+2$, $n\geq 3$. In this paper we give elementary proofs of the abelian group structure of $[X,Y]$ of homotopy classes of based maps from $X$ to $Y$, which was due to Baues and Schmidt. Furthermore, we determine the explicit generators associated to $[X,Y]$. As an application, we compute certain (sub)groups of self-homotopy equivalences of certain Chang complexes. |
| title | Homotopy classification of based maps between $\mathbf{A}_n^2$-complexes |
| topic | Algebraic Topology 55Q05, 55P10 |
| url | https://arxiv.org/abs/2008.03049 |