{"title":"高阶微分算子的相对 K 同调","authors":"Magnus Fries","doi":"10.1016/j.jfa.2024.110678","DOIUrl":null,"url":null,"abstract":"<div><p>We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order relative spectral triple gives rise to a relative <em>K</em>-homology cycle. In the case of an elliptic differential operator on a compact smooth manifold with boundary, we calculate the <em>K</em>-homology boundary map of the constructed relative <em>K</em>-homology cycle to obtain a generalization of the Baum-Douglas-Taylor index theorem.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022123624003665/pdfft?md5=e36d9b99bb0991b52d9d9a26d8663803&pid=1-s2.0-S0022123624003665-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Relative K-homology of higher-order differential operators\",\"authors\":\"Magnus Fries\",\"doi\":\"10.1016/j.jfa.2024.110678\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order relative spectral triple gives rise to a relative <em>K</em>-homology cycle. In the case of an elliptic differential operator on a compact smooth manifold with boundary, we calculate the <em>K</em>-homology boundary map of the constructed relative <em>K</em>-homology cycle to obtain a generalization of the Baum-Douglas-Taylor index theorem.</p></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0022123624003665/pdfft?md5=e36d9b99bb0991b52d9d9a26d8663803&pid=1-s2.0-S0022123624003665-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022123624003665\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123624003665","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Relative K-homology of higher-order differential operators
We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order relative spectral triple gives rise to a relative K-homology cycle. In the case of an elliptic differential operator on a compact smooth manifold with boundary, we calculate the K-homology boundary map of the constructed relative K-homology cycle to obtain a generalization of the Baum-Douglas-Taylor index theorem.
期刊介绍:
The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published.
Research Areas Include:
• Significant applications of functional analysis, including those to other areas of mathematics
• New developments in functional analysis
• Contributions to important problems in and challenges to functional analysis