{"title":"拓扑Hopf超代数中3-流形的亨宁斯型不变量","authors":"N. Ha","doi":"10.4171/qt/142","DOIUrl":null,"url":null,"abstract":"We prove the unrolled superalgebra $\\mathcal{U}_{\\xi}^{H}\\mathfrak{sl}(2|1)$ has a completion which is a ribbon superalgebra in a topological sense where $\\xi$ is a root of unity of odd order. Using this ribbon superalgebra we construct its universal invariant of links. We use it to construct an invariant of $3$-manifolds of Hennings type.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"100 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2018-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A Hennings type invariant of 3-manifolds from a topological Hopf superalgebra\",\"authors\":\"N. Ha\",\"doi\":\"10.4171/qt/142\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove the unrolled superalgebra $\\\\mathcal{U}_{\\\\xi}^{H}\\\\mathfrak{sl}(2|1)$ has a completion which is a ribbon superalgebra in a topological sense where $\\\\xi$ is a root of unity of odd order. Using this ribbon superalgebra we construct its universal invariant of links. We use it to construct an invariant of $3$-manifolds of Hennings type.\",\"PeriodicalId\":51331,\"journal\":{\"name\":\"Quantum Topology\",\"volume\":\"100 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2018-06-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/qt/142\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/qt/142","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Hennings type invariant of 3-manifolds from a topological Hopf superalgebra
We prove the unrolled superalgebra $\mathcal{U}_{\xi}^{H}\mathfrak{sl}(2|1)$ has a completion which is a ribbon superalgebra in a topological sense where $\xi$ is a root of unity of odd order. Using this ribbon superalgebra we construct its universal invariant of links. We use it to construct an invariant of $3$-manifolds of Hennings type.
期刊介绍:
Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular:
Low-dimensional Topology
Knot Theory
Jones Polynomial and Khovanov Homology
Topological Quantum Field Theory
Quantum Groups and Hopf Algebras
Mapping Class Groups and Teichmüller space
Categorification
Braid Groups and Braided Categories
Fusion Categories
Subfactors and Planar Algebras
Contact and Symplectic Topology
Topological Methods in Physics.