{"title":"固有作用的扭曲等变k理论中的补全定理","authors":"Noé Bárcenas, Mario Velásquez","doi":"10.1007/s40062-021-00299-z","DOIUrl":null,"url":null,"abstract":"<div><p>We compare different algebraic structures in twisted equivariant <i>K</i>-theory for proper actions of discrete groups. After the construction of a module structure over untwisted equivariant K-theory, we prove a completion Theorem of Atiyah–Segal type for twisted equivariant K-theory. Using a universal coefficient theorem, we prove a cocompletion Theorem for twisted Borel K-homology for discrete groups.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The completion theorem in twisted equivariant K-theory for proper actions\",\"authors\":\"Noé Bárcenas, Mario Velásquez\",\"doi\":\"10.1007/s40062-021-00299-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We compare different algebraic structures in twisted equivariant <i>K</i>-theory for proper actions of discrete groups. After the construction of a module structure over untwisted equivariant K-theory, we prove a completion Theorem of Atiyah–Segal type for twisted equivariant K-theory. Using a universal coefficient theorem, we prove a cocompletion Theorem for twisted Borel K-homology for discrete groups.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-01-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-021-00299-z\",\"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://link.springer.com/article/10.1007/s40062-021-00299-z","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
比较了离散群固有作用的扭曲等变k理论中不同的代数结构。在构造了非扭等变k理论的一个模结构后，证明了扭等变k理论的一个Atiyah-Segal型补全定理。利用一个普适系数定理，证明了离散群上扭曲Borel k -同调的一个协补定理。
The completion theorem in twisted equivariant K-theory for proper actions
We compare different algebraic structures in twisted equivariant K-theory for proper actions of discrete groups. After the construction of a module structure over untwisted equivariant K-theory, we prove a completion Theorem of Atiyah–Segal type for twisted equivariant K-theory. Using a universal coefficient theorem, we prove a cocompletion Theorem for twisted Borel K-homology for discrete groups.
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