TY - JOUR T1 - Some Properties of Aut$_∗(X)$ and the Subgroup Aut$_Σ(X)$ AU - Qian , Youhua AU - Chen , Shengmin JO - Communications in Mathematical Research VL - 2 SP - 97 EP - 103 PY - 2021 DA - 2021/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19291.html KW - self-homotopy equivalences, the wedge space, reducible. AB -

Let Aut$_∗(X)$ denote the group of homotopy classes of self-homotopy equivalences of $X$, which induce identity automorphisms of homology group. We describe a decomposition of Aut$_∗(X_1∨· · ·∨X_n)$ as a product of its simpler subgroups. We consider the subgroup Aut$_Σ(X)$ of all self homotopy classes α of $X$ such that $Σα = 1_{ΣX} : ΣX → ΣX$, and also give some properties of Aut$_Σ(X)$.