拓扑复杂性的Lusternik-Schnirelmann理论

IF 0.7 4区数学 Q2 MATHEMATICS

Topological Methods in Nonlinear Analysis Pub Date : 2022-08-16 DOI:10.12775/tmna.2022.060

Norio Iwase

{"title":"拓扑复杂性的Lusternik-Schnirelmann理论","authors":"Norio Iwase","doi":"10.12775/tmna.2022.060","DOIUrl":null,"url":null,"abstract":"We are trying to look over the Lusternik-Schnirelmann theory (L-S theory, for short) and the Topological Complexity (TC, for short) as a natural extension of the L-S theory.\nIn particular, we focus on the impact of the ideas originated from E. Fadell and S. Husseini on both theories.\nMore precisely, we see how their ideas on a category weight and a relative category drive the L-S theory and the TC.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lusternik-Schnirelmann theory to topological complexity from $A_{\\\\infty}$-view point\",\"authors\":\"Norio Iwase\",\"doi\":\"10.12775/tmna.2022.060\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We are trying to look over the Lusternik-Schnirelmann theory (L-S theory, for short) and the Topological Complexity (TC, for short) as a natural extension of the L-S theory.\\nIn particular, we focus on the impact of the ideas originated from E. Fadell and S. Husseini on both theories.\\nMore precisely, we see how their ideas on a category weight and a relative category drive the L-S theory and the TC.\",\"PeriodicalId\":23130,\"journal\":{\"name\":\"Topological Methods in Nonlinear Analysis\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topological Methods in Nonlinear Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.12775/tmna.2022.060\",\"RegionNum\":4,\"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":"Topological Methods in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12775/tmna.2022.060","RegionNum":4,"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

我们试图将Lusternik-Schnirelmann理论（简称L-S理论）和拓扑复杂性（简称TC）视为L-S理论的自然扩展。我们特别关注法德尔和侯赛尼的思想对这两种理论的影响。更准确地说，我们看到了他们关于范畴权重和相对范畴的想法是如何推动L-S理论和TC的。

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

Lusternik-Schnirelmann theory to topological complexity from $A_{\infty}$-view point

We are trying to look over the Lusternik-Schnirelmann theory (L-S theory, for short) and the Topological Complexity (TC, for short) as a natural extension of the L-S theory. In particular, we focus on the impact of the ideas originated from E. Fadell and S. Husseini on both theories. More precisely, we see how their ideas on a category weight and a relative category drive the L-S theory and the TC.

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

Topological Methods in Nonlinear Analysis 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.