三流形沿环面结整形的量子不变量

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2020-11-11 DOI:10.4171/qt/175

H. Murakami, Anh T. Tran

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引用次数: 0

摘要

研究了沿环面结用积分Dehn手术得到的Seifert纤维空间的Witten-Reshetikhin-Turaev不变量的渐近性，该不变量与n$-奇数n$的单位根的平方有关。我们证明了它可以被描述为与基本群到二维复特殊线性群的表示相关的chen - simons不变量和扭曲的Reidemeister扭转的和。

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Quantum invariants of three-manifolds obtained by surgeries along torus knots

We study the asymptotic behavior of the Witten-Reshetikhin-Turaev invariant associated with the square of the $n$-th root of unity with odd $n$ for a Seifert fibered space obtained by an integral Dehn surgery along a torus knot. We show that it can be described as a sum of the Chern-Simons invariants and the twisted Reidemeister torsions both associated with representations of the fundamental group to the two-dimensional complex special linear group.

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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.