非紧致曲面、三角形和刚性

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-04-30 DOI:10.1112/blms.70083

Stephen C. Power

{"title":"非紧致曲面、三角形和刚性","authors":"Stephen C. Power","doi":"10.1112/blms.70083","DOIUrl":null,"url":null,"abstract":"Every noncompact surface is shown to have a (3,6)-tight triangulation, and applications are given to the generic rigidity of countable bar-joint frameworks in <math>\n <semantics>\n <msup>\n <mi>R</mi>\n <mn>3</mn>\n </msup>\n <annotation>${\\mathbb {R}}^3$</annotation>\n </semantics></math>. In particular, every noncompact surface has a (3,6)-tight triangulation that is minimally 3-rigid. A simplification of Richards' proof of Kerékjártó's classification of noncompact surfaces is also given.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2097-2115"},"PeriodicalIF":0.9000,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70083","citationCount":"0","resultStr":"{\"title\":\"Noncompact surfaces, triangulations and rigidity\",\"authors\":\"Stephen C. Power\",\"doi\":\"10.1112/blms.70083\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Every noncompact surface is shown to have a (3,6)-tight triangulation, and applications are given to the generic rigidity of countable bar-joint frameworks in <math>\\n <semantics>\\n <msup>\\n <mi>R</mi>\\n <mn>3</mn>\\n </msup>\\n <annotation>${\\\\mathbb {R}}^3$</annotation>\\n </semantics></math>. In particular, every noncompact surface has a (3,6)-tight triangulation that is minimally 3-rigid. A simplification of Richards' proof of Kerékjártó's classification of noncompact surfaces is also given.\",\"PeriodicalId\":55298,\"journal\":{\"name\":\"Bulletin of the London Mathematical Society\",\"volume\":\"57 7\",\"pages\":\"2097-2115\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70083\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the London Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.70083\",\"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://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.70083","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

证明了每个非紧曲面都具有（3,6）紧三角化，并给出了r3 ${\mathbb {R}}^3$中可数杆节点框架的一般刚度的应用。特别地，每个非紧曲面都具有最小3刚性的（3,6）紧三角剖分。对Richards关于Kerékjártó非紧曲面分类的证明进行了简化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Noncompact surfaces, triangulations and rigidity

查看原文本刊更多论文

Noncompact surfaces, triangulations and rigidity

Every noncompact surface is shown to have a (3,6)-tight triangulation, and applications are given to the generic rigidity of countable bar-joint frameworks in $R^{3}$ . In particular, every noncompact surface has a (3,6)-tight triangulation that is minimally 3-rigid. A simplification of Richards' proof of Kerékjártó's classification of noncompact surfaces is also given.

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