Quantum decorated character stacks

Abstract

We initiate the study of decorated character stacks and their quantizations using the framework of stratified factorization homology. We thereby extend the construction by Fock and Goncharov of (quantum) decorated character varieties to encompass also the stacky points, in a way that is both compatible with cutting and gluing and equivariant with respect to canonical actions of the modular group of the surface. In the cases $G=S{L}_2,PG{L}_2$ we construct a system of categorical charts and flips on the quantum decorated character stacks which generalize the well--known cluster structures on the Fock--Goncharov moduli spaces.

References in corpus (6)

• The quantum dilogarithm and representations quantum cluster varieties
• Combinatorial quantization of the Hamiltonian Chern-Simons theory I
• Integrating quantum groups over surfaces
• Quantum geometry of moduli spaces of local systems and representation theory
• Cluster Structures on Higher Teichmuller Spaces for Classical Groups
• Excision of Skein Categories and Factorisation Homology