{"title":"变形G2-instantons/ Donaldson-Thomas连接的例子","authors":"Jason D. Lotay, Gonçalo Oliveira","doi":"10.5802/aif.3465","DOIUrl":null,"url":null,"abstract":"In this note, we provide the first non-trivial examples of deformed G_2-instantons, originally called deformed Donaldson-Thomas connections. As a consequence, we see how deformed G_2-instantons can be used to distinguish between nearly parallel G_2-structures and isometric G_2-structures on 3-Sasakian 7-manifolds. Our examples give non-trivial deformed G_2-instantons with obstructed deformation theory and situations where the moduli space of deformed G_2-instantons has components of different dimensions. We finally study the relation between our examples and a Chern-Simons type functional which has deformed G_2-instantons as critical points.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2020-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Examples of deformed G2-instantons/Donaldson–Thomas connections\",\"authors\":\"Jason D. Lotay, Gonçalo Oliveira\",\"doi\":\"10.5802/aif.3465\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note, we provide the first non-trivial examples of deformed G_2-instantons, originally called deformed Donaldson-Thomas connections. As a consequence, we see how deformed G_2-instantons can be used to distinguish between nearly parallel G_2-structures and isometric G_2-structures on 3-Sasakian 7-manifolds. Our examples give non-trivial deformed G_2-instantons with obstructed deformation theory and situations where the moduli space of deformed G_2-instantons has components of different dimensions. We finally study the relation between our examples and a Chern-Simons type functional which has deformed G_2-instantons as critical points.\",\"PeriodicalId\":50781,\"journal\":{\"name\":\"Annales De L Institut Fourier\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2020-07-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales De L Institut Fourier\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/aif.3465\",\"RegionNum\":4,\"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":"Annales De L Institut Fourier","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/aif.3465","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Examples of deformed G2-instantons/Donaldson–Thomas connections
In this note, we provide the first non-trivial examples of deformed G_2-instantons, originally called deformed Donaldson-Thomas connections. As a consequence, we see how deformed G_2-instantons can be used to distinguish between nearly parallel G_2-structures and isometric G_2-structures on 3-Sasakian 7-manifolds. Our examples give non-trivial deformed G_2-instantons with obstructed deformation theory and situations where the moduli space of deformed G_2-instantons has components of different dimensions. We finally study the relation between our examples and a Chern-Simons type functional which has deformed G_2-instantons as critical points.
期刊介绍：
The Annales de l’Institut Fourier aim at publishing original papers of a high level in all fields of mathematics, either in English or in French.
The Editorial Board encourages submission of articles containing an original and important result, or presenting a new proof of a central result in a domain of mathematics. Also, the Annales de l’Institut Fourier being a general purpose journal, highly specialized articles can only be accepted if their exposition makes them accessible to a larger audience.
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