Knot lattice homology and $q$-series invariants for plumbed knot complements
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909144970166272 |
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| author | Akhmechet, Rostislav Johnson, Peter K. Park, Sunghyuk |
| author_facet | Akhmechet, Rostislav Johnson, Peter K. Park, Sunghyuk |
| contents | We introduce an invariant of negative definite plumbed knot complements unifying knot lattice homology, due to Ozsváth, Stipsicz, and Szabó, and the BPS $q$-series of Gukov and Manolescu. This invariant is a natural extension of weighted graded roots of negative definite plumbed 3-manifolds introduced earlier by the first two authors and Krushkal. We prove a surgery formula relating our invariant with the weighted graded root of the surgered 3-manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14461 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Knot lattice homology and $q$-series invariants for plumbed knot complements Akhmechet, Rostislav Johnson, Peter K. Park, Sunghyuk Geometric Topology Quantum Algebra 57K31 (Primary) 57K18, 57K16 (Secondary) We introduce an invariant of negative definite plumbed knot complements unifying knot lattice homology, due to Ozsváth, Stipsicz, and Szabó, and the BPS $q$-series of Gukov and Manolescu. This invariant is a natural extension of weighted graded roots of negative definite plumbed 3-manifolds introduced earlier by the first two authors and Krushkal. We prove a surgery formula relating our invariant with the weighted graded root of the surgered 3-manifold. |
| title | Knot lattice homology and $q$-series invariants for plumbed knot complements |
| topic | Geometric Topology Quantum Algebra 57K31 (Primary) 57K18, 57K16 (Secondary) |
| url | https://arxiv.org/abs/2403.14461 |