{"title":"指数定理的一个简短证明,2","authors":"Yavar Abdolmaleki, Dan Kucerovsky","doi":"10.4171/jncg/524","DOIUrl":null,"url":null,"abstract":"We introduce a slight modification of the usual equivariant $KK$-theory. We use this to give a $KK$-theoretical proof of an equivariant index theorem for Dirac-Schrodinger operators on a non-compact manifold of nowhere positive curvature. We incidentally show that the boundary of Dirac is Dirac; generalizing earlier work of Baum and coworkers, and a result of Higson and Roe.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"9 3","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A short proof of an index theorem, II\",\"authors\":\"Yavar Abdolmaleki, Dan Kucerovsky\",\"doi\":\"10.4171/jncg/524\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a slight modification of the usual equivariant $KK$-theory. We use this to give a $KK$-theoretical proof of an equivariant index theorem for Dirac-Schrodinger operators on a non-compact manifold of nowhere positive curvature. We incidentally show that the boundary of Dirac is Dirac; generalizing earlier work of Baum and coworkers, and a result of Higson and Roe.\",\"PeriodicalId\":54780,\"journal\":{\"name\":\"Journal of Noncommutative Geometry\",\"volume\":\"9 3\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Noncommutative Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/jncg/524\",\"RegionNum\":2,\"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":"Journal of Noncommutative Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/jncg/524","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We introduce a slight modification of the usual equivariant $KK$-theory. We use this to give a $KK$-theoretical proof of an equivariant index theorem for Dirac-Schrodinger operators on a non-compact manifold of nowhere positive curvature. We incidentally show that the boundary of Dirac is Dirac; generalizing earlier work of Baum and coworkers, and a result of Higson and Roe.
期刊介绍:
The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular:
Hochschild and cyclic cohomology
K-theory and index theory
Measure theory and topology of noncommutative spaces, operator algebras
Spectral geometry of noncommutative spaces
Noncommutative algebraic geometry
Hopf algebras and quantum groups
Foliations, groupoids, stacks, gerbes
Deformations and quantization
Noncommutative spaces in number theory and arithmetic geometry
Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.