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A Quantum trace map for 3-manifolds

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arxiv 2403.12424 v1 pith:F3VLHSCK submitted 2024-03-19 math.GT hep-th

Stavros Garoufalidis , Tao Yu This is my paper · ORCID
classification math.GThep-th
keywords quantumtracemoduletorusbonahonboundarycomponentsconstructed
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We define a quantum trace map from the skein module of a 3-manifold with torus boundary components to a module (left and right quotient of a quantum torus) constructed from an ideal triangulation. Our map is a 3-dimensional version of the well-known quantum trace map on surfaces introduced by Bonahon and Wong and further developed by L\^e.

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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. Compatibility of quantum trace and UV-IR maps

    math.GT 2025-09 conditional novelty 8.0 of 10

    Quantum trace and quantum UV-IR maps fit into a natural commutative square; the surface case proves the Neitzke-Yan conjecture and the 3-manifold case recovers the 3d quantum trace map from the UV-IR map.

  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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