Volume 25, Issue 2
Some Properties of Aut$_∗(X)$ and the Subgroup Aut$_Σ(X)$

Commun. Math. Res., 25 (2009), pp. 97-103.

Published online: 2021-06

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• Abstract

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$_Σ(X)$.

• Keywords

self-homotopy equivalences, the wedge space, reducible.

• AMS Subject Headings

55P10

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COPYRIGHT: © Global Science Press

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@Article{CMR-25-97, author = {Youhua and Qian and and 18118 and and Youhua Qian and Shengmin and Chen and and 18119 and and Shengmin Chen}, title = {Some Properties of Aut$_∗(X)$ and the Subgroup Aut$_Σ(X)$}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {2}, pages = {97--103}, abstract = {

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$_Σ(X)$.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19291.html} }
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$_Σ(X)$.

YouhuaQian & ShengminChen. (2021). Some Properties of Aut$_∗(X)$ and the Subgroup Aut$_Σ(X)$. Communications in Mathematical Research . 25 (2). 97-103. doi:
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