论文标题
在2个连接和6维的CW复合物的自我态度等效上
On the group of self-homotopy equivalences of a 2-connected and 6-dimensional CW-complex
论文作者
论文摘要
令$ x $为a \ text {\ rm {2}} - 连接和\ text {\ rm {6}} - dimensional cw-complex $ x $，使得$ h_ {3}（x）（x）\ outimes \ z__2 = 0 $。本文旨在描述$ x $ modulo的$ \ e（x）$（x）$ $ x $ modulo的正常子组$ \ e _ {*}（x）（x）$的元素，这些元素诱导同源性群体的身份。利用$ x $的Whitehead精确顺序，由Wes $（x）$表示，我们定义了$γ$ -Automortomorphisms wes $（x）$的$γ\ Mathcal {s}（x）$，我们证明了$ \ e（x）/\ e（x）/\ e _*（x）/\ e _*（x）
Let $X$ be a \text{\rm{2}}-connected and \text{\rm{6}}-dimensional CW-complex $X$ such that $H_{3}(X)\otimes\Z_2=0$. This paper aims to describe the group $\E(X)$ of the self-homotopy equivalences of $X$ modulo its normal subgroup $\E_{*}(X)$ of the elements that induce the identity on the homology groups. Making use of the Whitehead exact sequence of $X$, denoted by WES$(X)$, we define the group $Γ\mathcal{S}(X)$ of $Γ$-automorphisms of WES$(X)$ and we prove that $\E(X)/\E_*(X)\cong Γ\mathcal{S}(X).$
