Let BPUn be the classifying space of PUn, the projective unitary group of order n, for n > 1. We use a Serre spectral sequence to determine the ring structure of H∗(BPU n; ℤ) up to degree 10, as well as a family of distinguished elements of H2p+2(BPU n; ℤ), for each prime divisor p of n. We also study the primitive elements of H∗(BU n; ℤ) as a comodule over H∗(K(ℤ, 2); ℤ), where the comodule structure is given by an action of K(ℤ, 2) ≃BS1 on BUn corresponding to the action of taking the tensor product of a complex line bundle and an n-dimensional complex vector bundle.

中文翻译：

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射影酉群分类空间的上同调

让BPUn是的分类空间聚氨酯n, 射影酉群n， 为了n > 1. 我们使用 Serre 谱序列来确定H*(BPU n; ℤ)达到学位10，以及一系列杰出的元素H2p+2(BPU n; ℤ), 对于每个素数除数p的n. 我们还研究了原始元素H*(事业部 n; ℤ)作为一个协模块H*(ķ(ℤ, 2); ℤ)，其中协模结构由以下动作给出ķ(ℤ, 2) ≃学士学位1在事业部n对应于取复线丛的张量积和n维复向量丛。