锚定泡沫和环空同源性

IF 0.6 3区数学 Q3 MATHEMATICS

Algebraic and Geometric Topology Pub Date : 2023-09-26 DOI:10.2140/agt.2023.23.3129

Rostislav Akhmechet, Mikhail Khovanov

{"title":"锚定泡沫和环空同源性","authors":"Rostislav Akhmechet, Mikhail Khovanov","doi":"10.2140/agt.2023.23.3129","DOIUrl":null,"url":null,"abstract":"We describe equivariant SL(2) and SL(3) homology for links in the solid torus via foam evaluation. The solid torus is replaced by 3-space with a distinguished line in it. Generators of state spaces for annular webs are represented by foams with boundary that may intersect the distinguished line; intersection points, called anchor points, contribute additional terms, reminiscent of square roots of the Hessian, to the foam evaluation. Both oriented and unoriented SL(3) foams are treated in the paper.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"43 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Anchored foams and annular homology\",\"authors\":\"Rostislav Akhmechet, Mikhail Khovanov\",\"doi\":\"10.2140/agt.2023.23.3129\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe equivariant SL(2) and SL(3) homology for links in the solid torus via foam evaluation. The solid torus is replaced by 3-space with a distinguished line in it. Generators of state spaces for annular webs are represented by foams with boundary that may intersect the distinguished line; intersection points, called anchor points, contribute additional terms, reminiscent of square roots of the Hessian, to the foam evaluation. Both oriented and unoriented SL(3) foams are treated in the paper.\",\"PeriodicalId\":50826,\"journal\":{\"name\":\"Algebraic and Geometric Topology\",\"volume\":\"43 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic and Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/agt.2023.23.3129\",\"RegionNum\":3,\"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":"Algebraic and Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/agt.2023.23.3129","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 5

摘要

通过泡沫评价，我们描述了固体环面中链接的等变SL(2)和SL(3)同源性。实体环面被三维空间替换，其中有一条不同的线。环形腹板状态空间的生成器用泡沫表示，泡沫的边界可能与区分线相交;交点，称为锚点，为泡沫评估提供了额外的术语，让人想起黑森的平方根。本文对定向和无取向SL(3)泡沫进行了处理。

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

Anchored foams and annular homology

We describe equivariant SL(2) and SL(3) homology for links in the solid torus via foam evaluation. The solid torus is replaced by 3-space with a distinguished line in it. Generators of state spaces for annular webs are represented by foams with boundary that may intersect the distinguished line; intersection points, called anchor points, contribute additional terms, reminiscent of square roots of the Hessian, to the foam evaluation. Both oriented and unoriented SL(3) foams are treated in the paper.

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

Algebraic and Geometric Topology 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebraic and Geometric Topology is a fully refereed journal covering all of topology, broadly understood.