A third construction of the 3d quantum trace map is proposed that agrees with Garoufalidis-Yu and relates to Panitch-Park via common subdivision of face suspensions and ideal tetrahedra into face cones.
3d Quantum Trace Map
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abstract
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.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proposes axiomatic framework for derived skein modules of 3-manifolds that recovers ordinary skein modules in degree zero, with computable formulas, Hochschild formula for Sigma x S^1, first computations, and finiteness via deformation quantization.
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On 3d Quantum Trace Maps
A third construction of the 3d quantum trace map is proposed that agrees with Garoufalidis-Yu and relates to Panitch-Park via common subdivision of face suspensions and ideal tetrahedra into face cones.
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Derived skein module
Proposes axiomatic framework for derived skein modules of 3-manifolds that recovers ordinary skein modules in degree zero, with computable formulas, Hochschild formula for Sigma x S^1, first computations, and finiteness via deformation quantization.