由Kauffman括号导出的非半简单三流形不变量

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology 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

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

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.