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Discover Yournastygirls.com Your Nasty Girls 霍普夫不变量 - 维基百科,自由的百科全书

Discover Yournastygirls.com Your Nasty Girls

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现在令 是一个稳定映射,即在约化垂纬函子下稳定。 的(稳定)几何霍普夫不变量

是从 到 映射的稳定 -等变同伦群中一个元素。这里稳定意为“在垂纬下稳定”,即通常等变同伦群在 上(或 ,如果你愿意)的正向极限;而 -作用是 的平凡作用与交换 中两个因子。如果我们令 表示典范对焦映射而 是恒等,则霍普夫不变量由下式定义:

这个映射原本是从 到 的映射,但在正向极限之下它成为映射的稳定同伦 -等变群的典型元素。

也有一个非稳定版本的霍普夫不变量 ,为此我们必须考虑向量空间 。

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