{"title":"2-配合物的对偶拟阵","authors":"Johannes Carmesin","doi":"10.1112/blms.70077","DOIUrl":null,"url":null,"abstract":"<p>We prove that simply connected local two-dimensional simplicial complexes embed in 3-space if and only if their dual matroids are graphic. Examples are provided that the assumptions of simply connectedness and locality are necessary. This may be regarded as a three-dimensional analogue of Whitney's planarity criterion from 1932.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2033-2044"},"PeriodicalIF":0.9000,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dual matroids of 2-complexes — Revisited\",\"authors\":\"Johannes Carmesin\",\"doi\":\"10.1112/blms.70077\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove that simply connected local two-dimensional simplicial complexes embed in 3-space if and only if their dual matroids are graphic. Examples are provided that the assumptions of simply connectedness and locality are necessary. This may be regarded as a three-dimensional analogue of Whitney's planarity criterion from 1932.</p>\",\"PeriodicalId\":55298,\"journal\":{\"name\":\"Bulletin of the London Mathematical Society\",\"volume\":\"57 7\",\"pages\":\"2033-2044\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-05-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the London Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/blms.70077\",\"RegionNum\":3,\"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":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.70077","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove that simply connected local two-dimensional simplicial complexes embed in 3-space if and only if their dual matroids are graphic. Examples are provided that the assumptions of simply connectedness and locality are necessary. This may be regarded as a three-dimensional analogue of Whitney's planarity criterion from 1932.