Compatibility of quantum trace and UV-IR maps
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911149247692800 |
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| author | Panitch, Samuel Park, Sunghyuk |
| author_facet | Panitch, Samuel Park, Sunghyuk |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compatibility of quantum trace and UV-IR maps Panitch, Samuel Park, Sunghyuk Geometric Topology Quantum Algebra 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. |
| title | Compatibility of quantum trace and UV-IR maps |
| topic | Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2509.09100 |