{"title":"关于叶状 3 球束不变量的说明","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":"{\"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}","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}
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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