维数小于 $15$ 的 $BPU_n$ 同调

arXiv - MATH - Algebraic Topology Pub Date : 2024-07-23 DOI:arxiv-2407.16297

Jiaxi Zha, Zhilei Zhang

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引用次数: 0

摘要

让 $PU_n$ 表示秩为 $n$ 的投影单元群，$BPU_n$ 是它的分类空间，当 $n>1$ 时。通过使用由纤维 $BU_n\to BPU_n\to K(\mathbb{Z},3)$ 引起的塞雷谱序列，我们计算了维数小于 $15$ 的 $BPU_n$ 的积分同调，除了维数为 $14$ 的 $4\mid n$ 。

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The cohomology of $BPU_n$ in dimensions less than $15$

Let $PU_n$ denote the projective unitary group of rank $n$ and $BPU_n$ be its classifying space, for $n>1$. By using the Serre spectral sequence induced by the fibration $BU_n\to BPU_n\to K(\mathbb{Z},3)$, we compute the integral cohomology of $BPU_n$ in dimensions less than $15$ except for $4\mid n$ in dimension $14$.

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arXiv - MATH - Algebraic Topology

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