主题:几何直观地介绍广义相对论的时空以及大爆炸模型 (0) -- changshou

2013-03-28 16:28:51晓兵
拓扑流形=摸著石頭過河, kind of

the followings are a rough kind of analogy, not real "math/physics", for the purpose of 图像

disclaimer:图像 is always an approximation, be careful and watch out, better to have different 图像 or have them upgraded.

1.

集合,势, a bounch of 石頭(kind of, or different 石頭 , 势=cardinality)

2

拓扑流形

"一个 Hausdorff 空间 X , 如果每一点都有一个开邻域与 n 维欧氏空间 E n 的一个开子集同胚, 就叫 X 为 n 维拓扑流形, 简称流形".

摸著石頭過河, 石頭 has some kind of "orders", some kind of 度量结构, largely global, "有没有洞、几个洞等"

3.

"拓扑流形再加上微分结构就称为微分流形. 也就是说, 除了上面的“局部欧氏化”, 还必须满足任两个相交的可欧氏化的开邻域, 其相交部分在两个同胚映射下的转换映射是 C r 可微的".

3.1

local 微分结构=局部欧氏化, no other choice

like china=tg, usa=5 "tg made in usa"

3.2

微分结构=任两个相交的可欧氏化的开邻域, 其相交部分在两个同胚映射下的转换映射, etc,kind of like usa=5 "tg made in usa", and from here on

广义相对论 , gauge theory;

4.

professor 陈省身: he linked global 度量结构, "有没有洞、几个洞等", with 微分结构 in 3.2, kind of, etc, big deal

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