Some link homologies in $ \mathbb{RP}^3 $
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914386391597056 |
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| author | Rushworth, William |
| author_facet | Rushworth, William |
| contents | We introduce extensions of Khovanov homology and the Lee and Bar-Natan spectral sequences for links in $ \mathbb{RP}^3 $. These extensions are distinct to those previously defined by Asaeda-Przytycki-Sikora (and Gabrovšek's generalization), Chen, and Manolescu-Willis. The new Lee and Bar-Natan theories each yield Rasmussen invariants (that are distinct to one another). The invariant extracted from the new Lee homology is distinct to that defined by Manolescu-Willis; it is unclear if the same is true for the new Bar-Natan homology and that defined by Chen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10832 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some link homologies in $ \mathbb{RP}^3 $ Rushworth, William Geometric Topology 57K18 We introduce extensions of Khovanov homology and the Lee and Bar-Natan spectral sequences for links in $ \mathbb{RP}^3 $. These extensions are distinct to those previously defined by Asaeda-Przytycki-Sikora (and Gabrovšek's generalization), Chen, and Manolescu-Willis. The new Lee and Bar-Natan theories each yield Rasmussen invariants (that are distinct to one another). The invariant extracted from the new Lee homology is distinct to that defined by Manolescu-Willis; it is unclear if the same is true for the new Bar-Natan homology and that defined by Chen. |
| title | Some link homologies in $ \mathbb{RP}^3 $ |
| topic | Geometric Topology 57K18 |
| url | https://arxiv.org/abs/2603.10832 |