Categorifying Quiver Linking/Unlinking using CoHA Modules
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929492551794688 |
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| author | van Garderen, Okke |
| author_facet | van Garderen, Okke |
| contents | The knots-quivers correspondence is a relation between knot invariants and enumerative invariants of quivers, which in particular translates the knot operations of linking and unlinking to a certain mutation operation on quivers. In this paper we show that the moduli spaces of a quiver and its linking/unlinking are naturally related, giving a purely representation theoretic interpretation of these operations. We obtain a relation between the cohomologies of these spaces which is moreover compatible with a natural action of the Cohomological Hall Algebra. The result is a categorification of quiver linking/unlinking at the level of CoHA modules. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_05605 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Categorifying Quiver Linking/Unlinking using CoHA Modules van Garderen, Okke Algebraic Geometry Representation Theory 16G20 (Primary), 14N35 (Secondary) The knots-quivers correspondence is a relation between knot invariants and enumerative invariants of quivers, which in particular translates the knot operations of linking and unlinking to a certain mutation operation on quivers. In this paper we show that the moduli spaces of a quiver and its linking/unlinking are naturally related, giving a purely representation theoretic interpretation of these operations. We obtain a relation between the cohomologies of these spaces which is moreover compatible with a natural action of the Cohomological Hall Algebra. The result is a categorification of quiver linking/unlinking at the level of CoHA modules. |
| title | Categorifying Quiver Linking/Unlinking using CoHA Modules |
| topic | Algebraic Geometry Representation Theory 16G20 (Primary), 14N35 (Secondary) |
| url | https://arxiv.org/abs/2409.05605 |