Abstract Let X be a finite type A n 2 {A_{n}^{2}} -polyhedron, n ≥ 2 {n\geq 2} . In this paper, we study the quotient group ℰ ⁢ ( X ) / ℰ * ⁢ ( X ) {\mathcal{E}(X)/\mathcal{E}_{*}(X)} , where ℰ ⁢ ( X ) {\mathcal{E}(X)} is the group of self-homotopy equivalences of X and ℰ * ⁢ ( X ) {\mathcal{E}_{*}(X)} the subgroup of self-homotopy equivalences inducing the identity on the homology groups of X. We show that not every group can be realised as ℰ ⁢ ( X ) {\mathcal{E}(X)} or ℰ ⁢ ( X ) / ℰ * ⁢ ( X ) {\mathcal{E}(X)/\mathcal{E}_{*}(X)} for X an A n 2 {A_{n}^{2}} -polyhedron, n ≥ 3 {n\geq 3} , and specific results are obtained for n = 2 {n=2} .

中文翻译：

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A n 2 {A_{n}^{2}} -多面体的自同伦等价群

Abstract 令 X 为有限类型 A n 2 {A_{n}^{2}} -polyhedron, n ≥ 2 {n\geq 2} 。在本文中，我们研究商群 ℰ ⁢ ( X ) / ℰ * ⁢ ( X ) {\mathcal{E}(X)/\mathcal{E}_{*}(X)} ，其中 ℰ ⁢ ( X ) {\mathcal{E}(X)} 是 X 的自同伦等价群， ℰ * ⁢ ( X ) {\mathcal{E}_{*}(X)} 是自同伦等价的子群X 的同调群上的恒等式。我们证明并不是每个群都可以实现为 ℰ ⁢ ( X ) {\mathcal{E}(X)} 或 ℰ ⁢ ( X ) / ℰ * ⁢ ( X ) {\mathcal {E}(X)/\mathcal{E}_{*}(X)} 对于 X an A n 2 {A_{n}^{2}} -多面体，n ≥ 3 {n\geq 3} ，和对于 n = 2 {n=2} 获得特定结果。