4-dimensional Skein modules, Handle attachments, and Tangles
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908842622713856 |
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| author | Martin, Gage Stelow, Mary Wattal, Mira |
| author_facet | Martin, Gage Stelow, Mary Wattal, Mira |
| contents | Skein lasagna modules are a recent tool developed for the study of 4-manifolds. We provide general formula for 1-, 2-, and 3-handle attachments for skein modules defined with any functorial link theory in $S^3 \times I$ generalizing existing formula of Chen, Manolescu-Neithalath, Manolescu-Walker-Wedrich, and Ren-Willis. These formula are derived from a complete description of the gluing homomorphism on skein modules. For this description, we introduce a variation of these skein modules in the presence of distinguished 3-manifolds in the boundary. A similar construction was recently introduced independently by Blackwell-Krushkal-Luo. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_17825 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | 4-dimensional Skein modules, Handle attachments, and Tangles Martin, Gage Stelow, Mary Wattal, Mira Geometric Topology Quantum Algebra 57K18, 57K41 Skein lasagna modules are a recent tool developed for the study of 4-manifolds. We provide general formula for 1-, 2-, and 3-handle attachments for skein modules defined with any functorial link theory in $S^3 \times I$ generalizing existing formula of Chen, Manolescu-Neithalath, Manolescu-Walker-Wedrich, and Ren-Willis. These formula are derived from a complete description of the gluing homomorphism on skein modules. For this description, we introduce a variation of these skein modules in the presence of distinguished 3-manifolds in the boundary. A similar construction was recently introduced independently by Blackwell-Krushkal-Luo. |
| title | 4-dimensional Skein modules, Handle attachments, and Tangles |
| topic | Geometric Topology Quantum Algebra 57K18, 57K41 |
| url | https://arxiv.org/abs/2602.17825 |