{"title":"The Atiyah-Singer Index Theorem for a Family of Fractional Dirac Operators on Spin Geometry","authors":"Rami Ahmad El-Nabulsi","doi":"10.1007/s00006-023-01270-2","DOIUrl":null,"url":null,"abstract":"<div><p>The Atiyah-Singer index formula for Dirac operators acting on the space of spinors put across a kind of topological invariant (<span>\\(\\hat{{A}}\\)</span> genus) of a closed spin manifold <span>\\({{\\mathcal {M}}}\\)</span>, hence offering a bridge between geometric and analytical aspects of the original spin manifold. In this study, we prove the index theorem for a family of fractional Dirac operators in particular for complex analytic coordinates.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 3","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-023-01270-2.pdf","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Clifford Algebras","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-023-01270-2","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
The Atiyah-Singer index formula for Dirac operators acting on the space of spinors put across a kind of topological invariant (\(\hat{{A}}\) genus) of a closed spin manifold \({{\mathcal {M}}}\), hence offering a bridge between geometric and analytical aspects of the original spin manifold. In this study, we prove the index theorem for a family of fractional Dirac operators in particular for complex analytic coordinates.
期刊介绍：
Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.
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