A topological proof of real and symplectic Bott periodicity theorem
A topological proof of real and symplectic Bott periodicity theorem
复制标题
实辛Bott周期定理的拓扑证明
DOI：
10.1215/kjm/1250517648
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发表时间：
2001
影响因子：
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通讯作者：
D. Kishimoto
中科院分区：
文献类型：
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作者：
D. Kishimoto
这篇文章的目的，正如标题一样，证明了实辛的Bott周期。作为引言，我将粗略地讲述证明的方式。由于本文的目标是BSP(Ω4BO)<0>和BO(Ω4BSp)<0>(对于拓扑空间X，X<n>表示X的n连通纤维空间，且设Prn：X<n>→X是普通投影)，所以我们必须构造λ：S∧BO→BSP和μ：S∧BSP→BO的映射。(为了做到这一点，我们使用了K理论这个词。)通过BO和BSP的一些良好的上同调性质，我们可以看出Adλ和Adμ几乎是同伦等价的，并且我们稍后去掉‘几乎’。
The purpose of this paper is, as in title, to prove real and symplectic Bott periodicity. For introduction I’ll tell, roughly, the way of the proof. Because the goal of this paper is that BSp (Ω4BO)〈0〉 and BO (Ω4BSp)〈0〉 (For a topological space X, X〈n〉 means n-connected fiber space of X and let prn : X〈n〉 → X be an ordinary projection.), we must construct maps that is λ : S ∧ BO → BSp and μ : S ∧ BSp → BO. (To do that, we use the word of K-theory.) By some of good cohomological properties of BO and BSp, we can tell the almost same thing as Ad λ and Ad μ are homotopy equivalence, and we remove ‘almost’ later.