具有小遗传密码的平面多边形空间具有较高的拓扑复杂度

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-09-04 DOI:10.1016/j.topol.2025.109575

Sutirtha Datta, Navnath Daundkar, Abhishek Sarkar

{"title":"具有小遗传密码的平面多边形空间具有较高的拓扑复杂度","authors":"Sutirtha Datta, Navnath Daundkar, Abhishek Sarkar","doi":"10.1016/j.topol.2025.109575","DOIUrl":null,"url":null,"abstract":"<div><div>We study the higher (sequential) topological complexity, a numerical homotopy invariant for the planar polygon spaces. For these spaces with a small genetic codes and dimension <em>m</em>, Davis showed that their topological complexity is either 2<em>m</em> or <span><math><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></math></span>. We extend these bounds to the setting of higher topological complexity. In particular, when <em>m</em> is power of 2, we show that the <em>k</em>-th higher topological complexity of these spaces is either <em>km</em> or <span><math><mi>k</mi><mi>m</mi><mo>+</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"375 ","pages":"Article 109575"},"PeriodicalIF":0.5000,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Higher topological complexity of planar polygon spaces having small genetic codes\",\"authors\":\"Sutirtha Datta, Navnath Daundkar, Abhishek Sarkar\",\"doi\":\"10.1016/j.topol.2025.109575\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We study the higher (sequential) topological complexity, a numerical homotopy invariant for the planar polygon spaces. For these spaces with a small genetic codes and dimension <em>m</em>, Davis showed that their topological complexity is either 2<em>m</em> or <span><math><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></math></span>. We extend these bounds to the setting of higher topological complexity. In particular, when <em>m</em> is power of 2, we show that the <em>k</em>-th higher topological complexity of these spaces is either <em>km</em> or <span><math><mi>k</mi><mi>m</mi><mo>+</mo><mn>1</mn></math></span>.</div></div>\",\"PeriodicalId\":51201,\"journal\":{\"name\":\"Topology and its Applications\",\"volume\":\"375 \",\"pages\":\"Article 109575\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2025-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166864125003736\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166864125003736","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了平面多边形空间的高（序）拓扑复杂度，一个数值同伦不变量。对于这些遗传密码较小、维数为m的空间，Davis证明了它们的拓扑复杂度为2m或2m+1。我们将这些界限扩展到更高拓扑复杂度的设置。特别地，当m是2的幂时，我们证明了这些空间的第k个高拓扑复杂度是km或km+1。

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

Higher topological complexity of planar polygon spaces having small genetic codes

We study the higher (sequential) topological complexity, a numerical homotopy invariant for the planar polygon spaces. For these spaces with a small genetic codes and dimension m, Davis showed that their topological complexity is either 2m or

2 m + 1

. We extend these bounds to the setting of higher topological complexity. In particular, when m is power of 2, we show that the k-th higher topological complexity of these spaces is either km or

k m + 1

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.