Higher Rank Ẑ and FK
We study q-series-valued invariants of 3-manifolds that depend on the choice of a root system . This is a natural generalization of the earlier works by Gukov-Pei-Putrov-Vafa [arXiv:1701.06567] and Gukov-Manolescu [arXiv:1904.06057], where they focused on the = SU(2) case. Although a full mathemati...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
| ISSN: | 1815-0659 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210706 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Higher Rank Ẑ and FK. Sunghyuk Park. SIGMA 16 (2020), 044, 17 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We study q-series-valued invariants of 3-manifolds that depend on the choice of a root system . This is a natural generalization of the earlier works by Gukov-Pei-Putrov-Vafa [arXiv:1701.06567] and Gukov-Manolescu [arXiv:1904.06057], where they focused on the = SU(2) case. Although a full mathematical definition for these ''invariants'' is lacking yet, we define Ẑ for negative definite plumbed 3-manifolds and FGK for torus knot complements. As in the = SU(2) case by Gukov and Manolescu, there is a surgery formula relating FGK to Ẑ of a Dehn surgery on the knot K. Furthermore, specializing to symmetric representations, FGK satisfies a recurrence relation given by the quantum A-polynomial for symmetric representations, which hints that there might be HOMFLY-PT analogues of these 3-manifold invariants.
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| ISSN: | 1815-0659 |