Khovanov Homology for Tangles in Connected Sums
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917321949315072 |
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| author | Du, Alan |
| author_facet | Du, Alan |
| contents | Khovanov homology is an invariant for links in the three sphere that categorizes the Jones polynomial. We extend Khovanov's construction to links in 3-manifolds that are connected sums of orientable interval bundles over surfaces. Cutting the 3-manifold along a separating sphere, we construct type D and type A structures that are invariants of tangles in the two halves following the work of Roberts. Gluing the type D and type A structures along the common boundary recovers the Khovanov homology of the link. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07337 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Khovanov Homology for Tangles in Connected Sums Du, Alan Geometric Topology 57K18 Khovanov homology is an invariant for links in the three sphere that categorizes the Jones polynomial. We extend Khovanov's construction to links in 3-manifolds that are connected sums of orientable interval bundles over surfaces. Cutting the 3-manifold along a separating sphere, we construct type D and type A structures that are invariants of tangles in the two halves following the work of Roberts. Gluing the type D and type A structures along the common boundary recovers the Khovanov homology of the link. |
| title | Khovanov Homology for Tangles in Connected Sums |
| topic | Geometric Topology 57K18 |
| url | https://arxiv.org/abs/2603.07337 |