{"title":"A note on invariants of foliated 3-sphere bundles","authors":"Nils Prigge","doi":"arxiv-2409.06408","DOIUrl":null,"url":null,"abstract":"In this note we prove that $H^*(\\text{BSO}(4);\\mathbb{Q})$ injects into the\ngroup cohomology of $\\text{Diff}^+(S^{3})$ with rational coefficients. The\nproof is based on an idea of Nariman who proved that the monomials in the Euler\nand Pontrjagin classes are nontrivial in\n$H^*(\\text{BDiff}_+^{\\delta}(S^{2n-1});\\mathbb{Q})$.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06408","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
In this note we prove that $H^*(\text{BSO}(4);\mathbb{Q})$ injects into the
group cohomology of $\text{Diff}^+(S^{3})$ with rational coefficients. The
proof is based on an idea of Nariman who proved that the monomials in the Euler
and Pontrjagin classes are nontrivial in
$H^*(\text{BDiff}_+^{\delta}(S^{2n-1});\mathbb{Q})$.
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