{"title":"时间反转对称Bloch束的微分几何不变量，II:低维“四元数”情况","authors":"Giuseppe De Nittis, Kiyonori Gomi","doi":"10.2140/agt.2023.23.2925","DOIUrl":null,"url":null,"abstract":"This paper is devoted to the construction of differential geometric invariants for the classification of \"Quaternionic\" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution that leaves fixed only a finite number of points, it is possible to prove that the Wess-Zumino term and the Chern-Simons invariant yield topological quantities able to distinguish between inequivalent realization of \"Quaternionic\" structures.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"23 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Differential geometric invariants for time-reversal symmetric Bloch bundles, II : The low-dimensional “quaternionic” case\",\"authors\":\"Giuseppe De Nittis, Kiyonori Gomi\",\"doi\":\"10.2140/agt.2023.23.2925\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is devoted to the construction of differential geometric invariants for the classification of \\\"Quaternionic\\\" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution that leaves fixed only a finite number of points, it is possible to prove that the Wess-Zumino term and the Chern-Simons invariant yield topological quantities able to distinguish between inequivalent realization of \\\"Quaternionic\\\" structures.\",\"PeriodicalId\":50826,\"journal\":{\"name\":\"Algebraic and Geometric Topology\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic and Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/agt.2023.23.2925\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic and Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/agt.2023.23.2925","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Differential geometric invariants for time-reversal symmetric Bloch bundles, II : The low-dimensional “quaternionic” case
This paper is devoted to the construction of differential geometric invariants for the classification of "Quaternionic" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution that leaves fixed only a finite number of points, it is possible to prove that the Wess-Zumino term and the Chern-Simons invariant yield topological quantities able to distinguish between inequivalent realization of "Quaternionic" structures.
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