Cluster Partition Function and Invariants of 3-Manifolds

被引：1
|
作者：
Romo, Mauricio [1 ]
机构：
[1] Inst Adv Study, Sch Nat Sci, Olden Lane, Princeton, NJ 08540 USA
来源：
CHINESE ANNALS OF MATHEMATICS SERIES B | 2017年 / 38卷 / 04期
关键词：
Chern-Simons theory; Knots; Cluster algebras; CHERN-SIMONS THEORY; HYPERBOLIC STRUCTURE; CHARACTER VARIETIES; VOLUME CONJECTURE; QUANTUM; QUANTIZATION; POLYNOMIALS; DUALITY;
D O I：
10.1007/s11401-017-1105-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The author reviews some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G. The author focuses on the case of G = SL(N, C) and M being a knot complement: M = S-3 \ K. The main result presented in this note is the cluster partition function, a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral for G = SL(N, C). He also reviews various applications and open questions regarding the cluster partition function and some of its relation with string theory.
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页码：937 / 962
页数：26
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