{"title":"乔伊斯广义库默构造中的共轭子曼形体","authors":"Dominik Gutwein","doi":"10.4310/pamq.2024.v20.n2.a7","DOIUrl":null,"url":null,"abstract":"This article constructs coassociative submanifolds in $\\mathrm{G}_2$-manifolds arising from Joyce’s generalised Kummer construction. The novelty compared to previous constructions is that these submanifolds all lie within the critical region of the $\\mathrm{G}_2$-manifold in which the metric degenerates. This forces the volume of the coassociatives to shrink to zero when the orbifold-limit is approached.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"243 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Coassociative submanifolds in Joyce's generalised Kummer constructions\",\"authors\":\"Dominik Gutwein\",\"doi\":\"10.4310/pamq.2024.v20.n2.a7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article constructs coassociative submanifolds in $\\\\mathrm{G}_2$-manifolds arising from Joyce’s generalised Kummer construction. The novelty compared to previous constructions is that these submanifolds all lie within the critical region of the $\\\\mathrm{G}_2$-manifold in which the metric degenerates. This forces the volume of the coassociatives to shrink to zero when the orbifold-limit is approached.\",\"PeriodicalId\":54526,\"journal\":{\"name\":\"Pure and Applied Mathematics Quarterly\",\"volume\":\"243 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-04-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pure and Applied Mathematics Quarterly\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/pamq.2024.v20.n2.a7\",\"RegionNum\":4,\"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":"Pure and Applied Mathematics Quarterly","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/pamq.2024.v20.n2.a7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Coassociative submanifolds in Joyce's generalised Kummer constructions
This article constructs coassociative submanifolds in $\mathrm{G}_2$-manifolds arising from Joyce’s generalised Kummer construction. The novelty compared to previous constructions is that these submanifolds all lie within the critical region of the $\mathrm{G}_2$-manifold in which the metric degenerates. This forces the volume of the coassociatives to shrink to zero when the orbifold-limit is approached.
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