由Kauffman括号导出的非半简单三流形不变量

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-07-21 DOI:10.4171/QT/164

M. Renzi, J. Murakami

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引用次数: 1

摘要

利用基于Temperley-Lieb代数和Kauffman括号多项式的纯组合方法，恢复了与$\mathfrak{sl}_2$的小量子群相关的闭取向3流形的非半单量子不变量族。这些不变量可以理解为Witten-Reshetikhin-Turaev不变量的一阶扩展，它可以按照我们的方法在有理同调球的情况下重新表述。

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Non-semisimple 3-manifold invariants derived from the Kauffman bracket

We recover the family of non-semisimple quantum invariants of closed oriented 3-manifolds associated with the small quantum group of $\mathfrak{sl}_2$ using purely combinatorial methods based on Temperley-Lieb algebras and Kauffman bracket polynomials. These invariants can be understood as a first-order extension of Witten-Reshetikhin-Turaev invariants, which can be reformulated following our approach in the case of rational homology spheres.

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来源期刊

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.