{"title":"The cohomology of $BPU_n$ in dimensions less than $15$","authors":"Jiaxi Zha, Zhilei Zhang","doi":"arxiv-2407.16297","DOIUrl":null,"url":null,"abstract":"Let $PU_n$ denote the projective unitary group of rank $n$ and $BPU_n$ be its\nclassifying space, for $n>1$. By using the Serre spectral sequence induced by\nthe fibration $BU_n\\to BPU_n\\to K(\\mathbb{Z},3)$, we compute the integral\ncohomology of $BPU_n$ in dimensions less than $15$ except for $4\\mid n$ in\ndimension $14$.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"6 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.16297","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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 $14$.