Cluster partition function and invariants of 3-manifolds

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, 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.

Keywords

Chern-Simons theory / Knots / Cluster algebras

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