{"title":"真实格拉斯曼流形的K理论","authors":"Sudeep Podder, Parameswaran Sankaran","doi":"10.4310/hha.2023.v25.n2.a17","DOIUrl":null,"url":null,"abstract":"Let $G_{n,k}$ denote the real Grassmann manifold of $k$-dimensional vector subspaces of $\\mathbb{R}^n$. We compute the complex $K$-ring of $G_{n,k}\\:$, up to a small indeterminacy, for all values of $n,k$ where $2 \\leqslant k \\leqslant n - 2$. When $n \\equiv 0 (\\operatorname{mod} 4), k \\equiv 1 (\\operatorname{mod} 2)$, we use the Hodgkin spectral sequence to determine the $K$-ring completely.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":"7 11","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"$K$-theory of real Grassmann manifolds\",\"authors\":\"Sudeep Podder, Parameswaran Sankaran\",\"doi\":\"10.4310/hha.2023.v25.n2.a17\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $G_{n,k}$ denote the real Grassmann manifold of $k$-dimensional vector subspaces of $\\\\mathbb{R}^n$. We compute the complex $K$-ring of $G_{n,k}\\\\:$, up to a small indeterminacy, for all values of $n,k$ where $2 \\\\leqslant k \\\\leqslant n - 2$. When $n \\\\equiv 0 (\\\\operatorname{mod} 4), k \\\\equiv 1 (\\\\operatorname{mod} 2)$, we use the Hodgkin spectral sequence to determine the $K$-ring completely.\",\"PeriodicalId\":55050,\"journal\":{\"name\":\"Homology Homotopy and Applications\",\"volume\":\"7 11\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-11-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Homology Homotopy and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/hha.2023.v25.n2.a17\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Homology Homotopy and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/hha.2023.v25.n2.a17","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
设$G_{n,k}$表示$\mathbb{R}^n$的$k$维向量子空间的实Grassmann流形。我们计算了$G_{n,k}\:$的复杂$K$ -环，直到一个小的不确定性，对于$n,k$的所有值，其中$2 \leqslant k \leqslant n - 2$。当$n \equiv 0 (\operatorname{mod} 4), k \equiv 1 (\operatorname{mod} 2)$时，我们使用霍奇金谱序列完全确定$K$ -环。
Let $G_{n,k}$ denote the real Grassmann manifold of $k$-dimensional vector subspaces of $\mathbb{R}^n$. We compute the complex $K$-ring of $G_{n,k}\:$, up to a small indeterminacy, for all values of $n,k$ where $2 \leqslant k \leqslant n - 2$. When $n \equiv 0 (\operatorname{mod} 4), k \equiv 1 (\operatorname{mod} 2)$, we use the Hodgkin spectral sequence to determine the $K$-ring completely.
期刊介绍：
Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.
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