用3柄Kirby图求$G$交叉编织球融合范畴的TQFT不变量

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Manuel Bärenz
{"title":"用3柄Kirby图求$G$交叉编织球融合范畴的TQFT不变量","authors":"Manuel Bärenz","doi":"10.4171/qt/183","DOIUrl":null,"url":null,"abstract":"A family of TQFTs parametrised by G-crossed braided spherical fusion categories has been defined recently as a state sum model and as a Hamiltonian lattice model. Concrete calculations of the resulting manifold invariants are scarce because of the combinatorial complexity of triangulations, if nothing else. Handle decompositions, and in particular Kirby diagrams are known to offer an economic and intuitive description of 4-manifolds. We show that if 3-handles are added to the picture, the state sum model can be conveniently redefined by translating Kirby diagrams into the graphical calculus of a G-crossed braided spherical fusion category. ","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Evaluating TQFT invariants from $G$-crossed braided spherical fusion categories via Kirby diagrams with 3-handles\",\"authors\":\"Manuel Bärenz\",\"doi\":\"10.4171/qt/183\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A family of TQFTs parametrised by G-crossed braided spherical fusion categories has been defined recently as a state sum model and as a Hamiltonian lattice model. Concrete calculations of the resulting manifold invariants are scarce because of the combinatorial complexity of triangulations, if nothing else. Handle decompositions, and in particular Kirby diagrams are known to offer an economic and intuitive description of 4-manifolds. We show that if 3-handles are added to the picture, the state sum model can be conveniently redefined by translating Kirby diagrams into the graphical calculus of a G-crossed braided spherical fusion category. \",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/qt/183\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/qt/183","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

摘要

由g交叉编织球融合范畴参数化的一类tqft最近被定义为状态和模型和哈密顿晶格模型。由于三角测量的组合复杂性(如果没有别的原因的话),所得到的流形不变量的具体计算很少。处理分解,特别是Kirby图提供了对4流形的经济和直观的描述。我们证明,如果在图像中添加3个手柄,则可以通过将Kirby图转换为g交叉编织球形融合类别的图形演算来方便地重新定义状态和模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Evaluating TQFT invariants from $G$-crossed braided spherical fusion categories via Kirby diagrams with 3-handles
A family of TQFTs parametrised by G-crossed braided spherical fusion categories has been defined recently as a state sum model and as a Hamiltonian lattice model. Concrete calculations of the resulting manifold invariants are scarce because of the combinatorial complexity of triangulations, if nothing else. Handle decompositions, and in particular Kirby diagrams are known to offer an economic and intuitive description of 4-manifolds. We show that if 3-handles are added to the picture, the state sum model can be conveniently redefined by translating Kirby diagrams into the graphical calculus of a G-crossed braided spherical fusion category.
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
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信