Homotopy classification of based maps between $\mathbf{A}_n^2$-complexes

Pengcheng Li

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arXiv · 2008.03049

Homotopy classification of based maps between $\mathbf{A}_n^2$-complexes

Pengcheng Li

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Abstract

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.

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Pengcheng Li. 2020-08-07. Homotopy classification of based maps between $\mathbf{A}_n^2$-complexes. https://arxiv.org/abs/2008.03049

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