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| Cluster Partition Function and Invariants of 3-Manifolds |
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Citation： |
Mauricio ROMO.Cluster Partition Function and Invariants of 3-Manifolds[J].Chinese Annals of Mathematics B,2017,38(4):937~962 |
| Page view： 2883
Net amount： 1359 |
Authors： |
Mauricio ROMO; |
Foundation： |
This work was supported by the U.S. Department of Energy
(No. DE-SC0009988). |
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| Abstract： |
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 $G=SL(N,\mathbb{C})$ and $M$ being a
knot complement: $M=S^{3}\setminus \mathcal{K}$. 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 $G=SL(N,\mathbb{C})$. He also
reviews various applications and open questions regarding the
cluster partition function and some of its relation with string
theory. |
Keywords： |
Chern-Simons theory, Knots, Cluster algebras |
Classification： |
17B40, 17B50 |
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