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Quantum decorated character stacks

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arxiv 2102.12283 v1 pith:RW62ZNDA submitted 2021-02-24 math.QA math.GTmath.RT

David Jordan , Ian Le , Gus Schrader , Alexander Shapiro This is my paper · ORCID
classification math.QAmath.GTmath.RT
keywords characterdecoratedquantumstacksactionscanonicalcasescategorical
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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 $G=SL_2,PGL_2$ 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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The algebraic modular functor conjecture in type $A_n$ quantum Teichm\"uller theory

    math.QA 2025-09 conditional novelty 8.0 of 10

    The algebraic modular functor conjecture of Fock and Goncharov, that cutting a surface yields a canonical gluing isomorphism of the associated quantum algebras, is proven for type A_n (G = PGL(n+1)).

  2. Parabolic skein modules

    math.QA 2025-05 conditional novelty 7.0 of 10

    Parabolic defect skein theory yields a new, triangulation-based definition and computation of the quantum A-ideal of knots, matching known classical limits.

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