Cluster Partition Function and Invariants of 3-manifolds

Mauricio Andrés Romo Jorquera

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2206.74018

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,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.
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  title={Cluster Partition Function and Invariants of 3-manifolds},
  author={Mauricio Andrés Romo Jorquera},
Mauricio Andrés Romo Jorquera. Cluster Partition Function and Invariants of 3-manifolds. 2017.
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