Cluster Partition Function and Invariants of 3-manifolds

Mauricio Romo

Cluster Partition Function and Invariants of 3-manifolds

High Energy Physics - Theory 2017-04-19 v2 Mathematical Physics math.MP

Authors: Mauricio Romo

Abstract

We review some recent developments in Chern-Simons theory on a hyperbolic 3-manifold $M$ with complex gauge group $G$ . We focus on the case $G=SL(N,\mathbb{C})$ and with $M$ a knot complement. 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. We also review various applications and open questions regarding the cluster partition function and some of its relation with string theory.

Keywords

Chern-Simons theory cluster partition function hyperbolic 3-manifold knot complement cluster algebra string theory

Cite

@article{arxiv.1704.00933,
  title  = {Cluster Partition Function and Invariants of 3-manifolds},
  author = {Mauricio Romo},
  journal= {arXiv preprint arXiv:1704.00933},
  year   = {2017}
}

Comments

26 pages, 1 figure, contribution to the proceedings of the workshop "Non-abelian Gauged Linear Sigma Model and Geometric Representation Theory" held at BICMR (Jun. 2015). To appear in a special issue of Chinese Annals of Mathematics, Series B; v2: reference added

Cluster Partition Function and Invariants of 3-manifolds

Abstract

Keywords

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