3d Quantum Trace Map

Samuel Panitch; Sunghyuk Park

3d Quantum Trace Map

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arxiv 2403.12850 v1 pith:4OEHYG7T submitted 2024-03-19 math.GT math.QA

Samuel Panitch , Sunghyuk Park This is my paper · ORCID

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We construct the 3d quantum trace map, a homomorphism from the Kauffman bracket skein module of an ideally triangulated 3-manifold to its (square root) quantum gluing module, thereby giving a precise relationship between the two quantizations of the character variety of ideally triangulated 3-manifolds. This map, whose existence was conjectured earlier by Agarwal, Gang, Lee, and Romo, is a natural 3-dimensional analog of the 2d quantum trace map of Bonahon and Wong. Our construction is based on the study of stated skein modules and their behavior under splitting, especially into face suspensions.

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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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