Relations between Witten-reshetikhin-turaev and non semi-simple sl(2) 3-manifold invariants
Relations between Witten-reshetikhin-turaev and non semi-simple sl(2) 3-manifold invariants
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Witten-reshetikhin-turaev 与非半单 sl(2) 3 流形不变量之间的关系
DOI：
10.2140/agt.2015.15.1363
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发表时间：
2013
影响因子：
0.7
通讯作者：
Bertrand Patureau
中科院分区：
文献类型：
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作者：
F. Costantino;Nathan Geer;Bertrand Patureau
Witten-Reshetikhin-Turaev不变量将S^3中环的Jones多项式推广到三维流形中的环的不变量。类似地，在前文中，作者构造了两个3-流形不变量N_r和N^0_r，它们将S^3中复数着色的环的Akutsu-Deguchi-Ohtsuki不变量推广到任意流形中的环。所有这些不变量都是基于量子群Uqsl2的表示理论，其中不变量N_r和N^0_r的定义使用了非标准的Uqsl2-模范畴，这不是半简单的。本文研究了第二不变量N^0_r，并讨论了它与WRT不变量的关系。特别地，我们证明了S^3中纽结的ADO不变量是其颜色的亚纯函数，并给出了它的留数与纽结的有色Jones多项式之间的强关系。然后，我们猜想N^0_r与WRT不变量之间有类似的关系。当3-流形M不是有理同调球面时，当M是S^3中的一个纽结上的有理同调球面时，或者当M是这些流形的连通和时，我们证明了这一猜想。
The Witten-Reshetikhin-Turaev invariants extend the Jones polynomials of links in S^3 to invariants of links in 3-manifolds. Similarly, in a preceding paper, the authors constructed two 3-manifold invariants N_r and N^0_r which extend the Akutsu-Deguchi-Ohtsuki invariant of links in S^3 colored by complex numbers to links in arbitrary manifolds. All these invariants are based on representation theory of the quantum group Uqsl2, where the definition of the invariants N_r and N^0_r uses a non-standard category of Uqsl2-modules which is not semi-simple. In this paper we study the second invariant N^0_r and consider its relationship with the WRT invariants. In particular, we show that the ADO invariant of a knot in S^3 is a meromorphic function of its color and we provide a strong relation between its residues and the colored Jones polynomials of the knot. Then we conjecture a similar relation between N^0_r and a WRT invariant. We prove this conjecture when the 3-manifold M is not a rational homology sphere and when M is a rational homology sphere obtained by surgery on a knot in S^3 or when M is a connected sum of such manifolds.
广义量子 6j 符号和有色亚历山大不变量
DOI：
--
发表时间：
2009
期刊：
影响因子：
--
作者：
Katsuya Miyake;Akinari Hoshi;Jun Murakami and Kiyokazu Nagatomo;Kiichiro Hashimoto;Jun Murakami;Jun Murakami
通讯作者：
Jun Murakami