{"title":"有限呈现群中的发小","authors":"Joseph MacManus","doi":"arxiv-2408.10748","DOIUrl":null,"url":null,"abstract":"We show that a finitely presented group virtually admits a planar Cayley\ngraph if and only if it is asymptotically minor-excluded, partially answering a\nconjecture of Georgakopoulos and Papasoglu in the affirmative.","PeriodicalId":501444,"journal":{"name":"arXiv - MATH - Metric Geometry","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fat minors in finitely presented groups\",\"authors\":\"Joseph MacManus\",\"doi\":\"arxiv-2408.10748\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that a finitely presented group virtually admits a planar Cayley\\ngraph if and only if it is asymptotically minor-excluded, partially answering a\\nconjecture of Georgakopoulos and Papasoglu in the affirmative.\",\"PeriodicalId\":501444,\"journal\":{\"name\":\"arXiv - MATH - Metric Geometry\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Metric Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.10748\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Metric Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.10748","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We show that a finitely presented group virtually admits a planar Cayley
graph if and only if it is asymptotically minor-excluded, partially answering a
conjecture of Georgakopoulos and Papasoglu in the affirmative.
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