Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2509.09100 |
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Inhaltsangabe:
- This paper studies the connection between the quantum trace map -- which maps the $\mathfrak{sl}_2$-skein module to the quantum Teichmüller space for surfaces and to the quantum gluing module for 3-manifolds -- and the quantum UV-IR map -- which maps the $\mathfrak{gl}_2$-skein module to the $\mathfrak{gl}_1$-skein module of the branched double cover. We show that the two maps are compatible in a precise sense, and that the compatibility map is natural under changes of triangulation; for surfaces, this resolves a conjecture of Neitzke and Yan. As a corollary, under a mild hypothesis on the 3-manifold, the quantum trace map can be recovered from the quantum UV-IR map, hence providing yet another construction of the recently introduced 3d quantum trace map.