{"title":"可分解Dixmier-Douady类的扭曲k理论构造","authors":"Antti J. Harju, J. Mickelsson","doi":"10.1017/IS014007001JKT274","DOIUrl":null,"url":null,"abstract":"Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed in the case when X is a product of a circle T and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral one form on T and an integral class in H(M,Z). This case was studied some time ago by V. Mathai, R. Melrose, and I.M. Singer. Our aim is to give an explicit construction for the twisted K-theory classes using a quantum field theory model, in the same spirit as the supersymmetric Wess-Zumino-Witten model is used for constructing (equivariant) twisted K-theory classes on compact Lie groups. Msc: 19L50, 53C08, 81T70","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"47 27 1","pages":"247-272"},"PeriodicalIF":0.0000,"publicationDate":"2012-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS014007001JKT274","citationCount":"8","resultStr":"{\"title\":\"Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class\",\"authors\":\"Antti J. Harju, J. Mickelsson\",\"doi\":\"10.1017/IS014007001JKT274\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed in the case when X is a product of a circle T and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral one form on T and an integral class in H(M,Z). This case was studied some time ago by V. Mathai, R. Melrose, and I.M. Singer. Our aim is to give an explicit construction for the twisted K-theory classes using a quantum field theory model, in the same spirit as the supersymmetric Wess-Zumino-Witten model is used for constructing (equivariant) twisted K-theory classes on compact Lie groups. Msc: 19L50, 53C08, 81T70\",\"PeriodicalId\":50167,\"journal\":{\"name\":\"Journal of K-Theory\",\"volume\":\"47 27 1\",\"pages\":\"247-272\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-08-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1017/IS014007001JKT274\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/IS014007001JKT274\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of K-Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/IS014007001JKT274","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class
Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed in the case when X is a product of a circle T and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral one form on T and an integral class in H(M,Z). This case was studied some time ago by V. Mathai, R. Melrose, and I.M. Singer. Our aim is to give an explicit construction for the twisted K-theory classes using a quantum field theory model, in the same spirit as the supersymmetric Wess-Zumino-Witten model is used for constructing (equivariant) twisted K-theory classes on compact Lie groups. Msc: 19L50, 53C08, 81T70
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