一种将柯比图转换为三分图的算法

IF 0.7 3区数学 Q2 MATHEMATICS

Pacific Journal of Mathematics Pub Date : 2021-10-31 DOI:10.2140/pjm.2022.318.109

Willi Kepplinger

{"title":"一种将柯比图转换为三分图的算法","authors":"Willi Kepplinger","doi":"10.2140/pjm.2022.318.109","DOIUrl":null,"url":null,"abstract":"We present an algorithm taking a Kirby diagram of a closed oriented $4$-manifold to a trisection diagram of the same manifold. This algorithm provides us with a large number of examples for trisection diagrams of closed oriented $4$-manifolds since many Kirby-diagrammatic descriptions of closed oriented $4$-manifolds are known. That being said, the algorithm does not necessarily provide particularly efficient trisection diagrams. We also extend this algorithm to work for the non-orientable case.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"An algorithm taking Kirby diagrams to trisection diagrams\",\"authors\":\"Willi Kepplinger\",\"doi\":\"10.2140/pjm.2022.318.109\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present an algorithm taking a Kirby diagram of a closed oriented $4$-manifold to a trisection diagram of the same manifold. This algorithm provides us with a large number of examples for trisection diagrams of closed oriented $4$-manifolds since many Kirby-diagrammatic descriptions of closed oriented $4$-manifolds are known. That being said, the algorithm does not necessarily provide particularly efficient trisection diagrams. We also extend this algorithm to work for the non-orientable case.\",\"PeriodicalId\":54651,\"journal\":{\"name\":\"Pacific Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pacific Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2140/pjm.2022.318.109\",\"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":"Pacific Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/pjm.2022.318.109","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: 4

摘要

我们提出了一种算法，将一个封闭的面向$4$流形的Kirby图转化为相同流形的三切分图。该算法为我们提供了大量的面向闭合$4$流形的三角图示例，因为许多面向闭合$4$流形的kirby图描述是已知的。也就是说，该算法不一定提供特别有效的三切分图。我们还将该算法扩展到非定向情况下。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

An algorithm taking Kirby diagrams to trisection diagrams

We present an algorithm taking a Kirby diagram of a closed oriented $4$-manifold to a trisection diagram of the same manifold. This algorithm provides us with a large number of examples for trisection diagrams of closed oriented $4$-manifolds since many Kirby-diagrammatic descriptions of closed oriented $4$-manifolds are known. That being said, the algorithm does not necessarily provide particularly efficient trisection diagrams. We also extend this algorithm to work for the non-orientable case.

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

Pacific Journal of Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Founded in 1951, PJM has published mathematics research for more than 60 years. PJM is run by mathematicians from the Pacific Rim. PJM aims to publish high-quality articles in all branches of mathematics, at low cost to libraries and individuals. The Pacific Journal of Mathematics is incorporated as a 501(c)(3) California nonprofit.