Root lattices and invariant series for plumbed 3-manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914449325031424 |
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| author | Moore, Allison H. Tarasca, Nicola |
| author_facet | Moore, Allison H. Tarasca, Nicola |
| contents | We study formal series which are invariants of plumbed 3-manifolds twisted by root lattices. These series extend the BPS $q$-series $\widehat{Z}(q)$ recently defined in Gukov-Pei-Putrov-Vafa, Gukov-Manolescu, Park, and further refined in Ri. We show that the series $\widehat{Z}(q)$ is unique in an appropriate sense and decomposes as the average of related series which are themselves invariant under the five Neumann moves amongst plumbing trees. Explicit computations are presented in the case of Brieskorn spheres and a non-Seifert manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Root lattices and invariant series for plumbed 3-manifolds Moore, Allison H. Tarasca, Nicola Geometric Topology Algebraic Geometry Quantum Algebra 57K31 (Primary), 57K16, 17B22 (Secondary) We study formal series which are invariants of plumbed 3-manifolds twisted by root lattices. These series extend the BPS $q$-series $\widehat{Z}(q)$ recently defined in Gukov-Pei-Putrov-Vafa, Gukov-Manolescu, Park, and further refined in Ri. We show that the series $\widehat{Z}(q)$ is unique in an appropriate sense and decomposes as the average of related series which are themselves invariant under the five Neumann moves amongst plumbing trees. Explicit computations are presented in the case of Brieskorn spheres and a non-Seifert manifold. |
| title | Root lattices and invariant series for plumbed 3-manifolds |
| topic | Geometric Topology Algebraic Geometry Quantum Algebra 57K31 (Primary), 57K16, 17B22 (Secondary) |
| url | https://arxiv.org/abs/2405.14972 |