{"title":"扩展曲面的有限自由作用","authors":"Rubén A. Hidalgo","doi":"10.1112/blms.13068","DOIUrl":null,"url":null,"abstract":"<p>We prove the existence of finite groups acting freely as orientation-preserving homeomorphisms on closed orientable surfaces that extend as a group of homeomorphisms of some compact orientable 3-manifold but that cannot extend to a handlebody. This solves a basic problem in low-dimensional equivariant topology going back to the work of Reni and Zimmermann in the mid-1990s.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 7","pages":"2495-2513"},"PeriodicalIF":0.8000,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Extending finite free actions of surfaces\",\"authors\":\"Rubén A. Hidalgo\",\"doi\":\"10.1112/blms.13068\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove the existence of finite groups acting freely as orientation-preserving homeomorphisms on closed orientable surfaces that extend as a group of homeomorphisms of some compact orientable 3-manifold but that cannot extend to a handlebody. This solves a basic problem in low-dimensional equivariant topology going back to the work of Reni and Zimmermann in the mid-1990s.</p>\",\"PeriodicalId\":55298,\"journal\":{\"name\":\"Bulletin of the London Mathematical Society\",\"volume\":\"56 7\",\"pages\":\"2495-2513\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-11\",\"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.13068\",\"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.13068","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove the existence of finite groups acting freely as orientation-preserving homeomorphisms on closed orientable surfaces that extend as a group of homeomorphisms of some compact orientable 3-manifold but that cannot extend to a handlebody. This solves a basic problem in low-dimensional equivariant topology going back to the work of Reni and Zimmermann in the mid-1990s.
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