典范局部平凡化

本书暂定概念：尚未进入正式概念库。下面是本书给出的定义原文。

定义 · 9.4 主丛

这一局部平凡化称为典范局部平凡化(canonical local trivialization)。按定义有 ${\varphi }_i(p,g)={\varphi }_i(p,e)g=s_i(p)g$。若 $p\in U_i\cap U_j$，则两个截面 $s_i(p)$ 与 $s_j(p)$ 通过过渡函数 $t_{ij}(p)$ 相联系，如下所示

$$\begin{array}{rl}{s}_i(p)& ={\varphi }_i(p,e)={\varphi }_j(p,t_{ji}(p)e)={\varphi }_j(p,t_{ji}(p))\\ & ={\varphi }_j(p,e)t_{ji}(p)=s_j(p)t_{ji}(p).\end{array}\text{\hspace{1em}(9.43)}$$

英文原文

This local trivialization is called the canonical local trivialization. By definition ${\varphi }_i(p,g)={\varphi }_i(p,e)g=s_i(p)g$ . If $p\in U_i\cap U_j$ , two sections $s_i(p)$ and $s_j(p)$ are related by the transition function $t_{ij}(p)$ as follows

$$\begin{array}{rl}{s}_i(p)& ={\varphi }_i(p,e)={\varphi }_j(p,t_{ji}(p)e)={\varphi }_j(p,t_{ji}(p))\\ & ={\varphi }_j(p,e)t_{ji}(p)=s_j(p)t_{ji}(p).\end{array}\text{\hspace{1em}(9.43)}$$

出处：9.4 主丛 · node a-2bc6d55996f955cdd7174157 · 源节点 SHA-256 6a5ab8cdcef225da…