{"title":"面向格拉斯曼流形 G͠ 2 t,3 的模 2 同调中的格氏基","authors":"Uroš A. Colović, Branislav I. Prvulović","doi":"10.1515/ms-2024-0015","DOIUrl":null,"url":null,"abstract":"For <jats:italic>n</jats:italic> a power of two, we give a complete description of the cohomology algebra <jats:italic>H</jats:italic> <jats:sup>*</jats:sup>(<jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub>; ℤ<jats:sub>2</jats:sub>) of the Grassmann manifold <jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub> of oriented 3-planes in ℝ<jats:sup> <jats:italic>n</jats:italic> </jats:sup>. We do this by finding a reduced Gröbner basis for an ideal closely related to this cohomology algebra. Using this Gröbner basis we also present an additive basis for <jats:italic>H</jats:italic> <jats:sup>*</jats:sup>(<jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub>; ℤ<jats:sub>2</jats:sub>).","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠ 2 t,3\",\"authors\":\"Uroš A. Colović, Branislav I. Prvulović\",\"doi\":\"10.1515/ms-2024-0015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For <jats:italic>n</jats:italic> a power of two, we give a complete description of the cohomology algebra <jats:italic>H</jats:italic> <jats:sup>*</jats:sup>(<jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub>; ℤ<jats:sub>2</jats:sub>) of the Grassmann manifold <jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub> of oriented 3-planes in ℝ<jats:sup> <jats:italic>n</jats:italic> </jats:sup>. We do this by finding a reduced Gröbner basis for an ideal closely related to this cohomology algebra. Using this Gröbner basis we also present an additive basis for <jats:italic>H</jats:italic> <jats:sup>*</jats:sup>(<jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub>; ℤ<jats:sub>2</jats:sub>).\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/ms-2024-0015\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ms-2024-0015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
对于 n 的 2 次幂，我们给出了对ℝ n 中定向 3 平面的格拉斯曼流形 G͠ n,3 的同调代数 H *(G͠ n,3; ℤ2)的完整描述。为此，我们要为与这个同调代数密切相关的理想找到一个还原的格氏基。利用这个格氏基，我们还提出了 H *(G͠ n,3; ℤ2)的加法基。
Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠ 2 t,3
For n a power of two, we give a complete description of the cohomology algebra H*(G͠n,3; ℤ2) of the Grassmann manifold G͠n,3 of oriented 3-planes in ℝn. We do this by finding a reduced Gröbner basis for an ideal closely related to this cohomology algebra. Using this Gröbner basis we also present an additive basis for H*(G͠n,3; ℤ2).
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