表面覆盖物

arXiv - MATH - Geometric Topology Pub Date : 2024-09-06 DOI:arxiv-2409.03967

Ian Biringer, Yassin Chandran, Tommaso Cremaschi, Jing Tao, Nicholas G. Vlamis, Mujie Wang, Brandis Whitfield

{"title":"表面覆盖物","authors":"Ian Biringer, Yassin Chandran, Tommaso Cremaschi, Jing Tao, Nicholas G. Vlamis, Mujie Wang, Brandis Whitfield","doi":"arxiv-2409.03967","DOIUrl":null,"url":null,"abstract":"We study the homeomorphism types of certain covers of (always orientable)\nsurfaces, usually of infinite-type. We show that every surface with non-abelian\nfundamental group is covered by every noncompact surface, we identify the\nuniversal abelian covers and the $\\mathbb{Z}/n\\mathbb{Z}$-homology covers of\nsurfaces, and we show that non-locally finite characteristic covers of surfaces\nhave four possible homeomorphism types.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Covers of surfaces\",\"authors\":\"Ian Biringer, Yassin Chandran, Tommaso Cremaschi, Jing Tao, Nicholas G. Vlamis, Mujie Wang, Brandis Whitfield\",\"doi\":\"arxiv-2409.03967\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the homeomorphism types of certain covers of (always orientable)\\nsurfaces, usually of infinite-type. We show that every surface with non-abelian\\nfundamental group is covered by every noncompact surface, we identify the\\nuniversal abelian covers and the $\\\\mathbb{Z}/n\\\\mathbb{Z}$-homology covers of\\nsurfaces, and we show that non-locally finite characteristic covers of surfaces\\nhave four possible homeomorphism types.\",\"PeriodicalId\":501271,\"journal\":{\"name\":\"arXiv - MATH - Geometric Topology\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.03967\",\"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 - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.03967","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了（总是可定向的）曲面的某些盖的同构类型，通常是无穷型的。我们证明了每一个具有非阿贝尔基群的曲面都被每一个非紧凑曲面所覆盖，我们识别了曲面的普遍非阿贝尔覆盖和$\mathbb{Z}/n\mathbb{Z}$同构覆盖，并证明了曲面的非局部有限特征覆盖有四种可能的同构类型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Covers of surfaces

We study the homeomorphism types of certain covers of (always orientable) surfaces, usually of infinite-type. We show that every surface with non-abelian fundamental group is covered by every noncompact surface, we identify the universal abelian covers and the $\mathbb{Z}/n\mathbb{Z}$-homology covers of surfaces, and we show that non-locally finite characteristic covers of surfaces have four possible homeomorphism types.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Geometric Topology

自引率

0.00%

发文量

期刊最新文献

Exotic Dehn twists and homotopy coherent group actions $\infty$-operadic foundations for embedding calculus Simultaneous Uniformization and Algebraic Correspondences A note on lattice knots Enhanced Hantzsche Theorem