Homotopy classification of maps between An2\mathbf{A}_n^2-complexes

In this article, the author improves Baues's homotopy classification of maps between indecomposable $(n-1)$-connected $(n+2)$ dimensional finite CW-complexes $X,Y,n>3$, by finding a generating set for any abelian group $[X,Y]$. Using these generators, the author firstly finds splitting cofiber sequences which imply Zhu-Pan's decomposability result of smash products of the complexes, and secondly, obtains partial results on the groups of homotopy classes of self-homotopy equivalences of the complexes and some of their natural subgroups.Comment: 38 pages, partial work of PhD thesis, any related comments are welcom