{"title":"周期方钉问题的解决方案","authors":"Cole Hugelmeyer","doi":"arxiv-2407.20412","DOIUrl":null,"url":null,"abstract":"We resolve the periodic square peg problem using a simple Lagrangian Floer\nhomology argument. Inscribed squares are interpreted as intersections between\ntwo non-displaceable Lagrangian sub-manifolds of a symplectic 4-torus.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":"124 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Solution to the Periodic Square Peg Problem\",\"authors\":\"Cole Hugelmeyer\",\"doi\":\"arxiv-2407.20412\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We resolve the periodic square peg problem using a simple Lagrangian Floer\\nhomology argument. Inscribed squares are interpreted as intersections between\\ntwo non-displaceable Lagrangian sub-manifolds of a symplectic 4-torus.\",\"PeriodicalId\":501155,\"journal\":{\"name\":\"arXiv - MATH - Symplectic Geometry\",\"volume\":\"124 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Symplectic Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.20412\",\"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 - Symplectic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.20412","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We resolve the periodic square peg problem using a simple Lagrangian Floer
homology argument. Inscribed squares are interpreted as intersections between
two non-displaceable Lagrangian sub-manifolds of a symplectic 4-torus.
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