Parabolic skein modules
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908372836548608 |
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| author | Brown, Jennifer Jordan, David |
| author_facet | Brown, Jennifer Jordan, David |
| contents | We develop skein theory for 3-manifolds in the presence of codimension-one defects, focusing especially on defects arising from parabolic induction/restriction for quantum groups. We use these defects as a model for the quantum decorated character stacks of arXiv:2102.12283, thus extending them to 3-manifolds with surface defects. As a special case we obtain knot invariants closely related to the ``quantum $A$-polynomial", and we give a concrete method for computation resembling the approach of Dimofte and collaborators based on ideal triangulations and gluing equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parabolic skein modules Brown, Jennifer Jordan, David Quantum Algebra Geometric Topology Representation Theory 57K31 (primary) 81T45, 20G42 (secondary) We develop skein theory for 3-manifolds in the presence of codimension-one defects, focusing especially on defects arising from parabolic induction/restriction for quantum groups. We use these defects as a model for the quantum decorated character stacks of arXiv:2102.12283, thus extending them to 3-manifolds with surface defects. As a special case we obtain knot invariants closely related to the ``quantum $A$-polynomial", and we give a concrete method for computation resembling the approach of Dimofte and collaborators based on ideal triangulations and gluing equations. |
| title | Parabolic skein modules |
| topic | Quantum Algebra Geometric Topology Representation Theory 57K31 (primary) 81T45, 20G42 (secondary) |
| url | https://arxiv.org/abs/2505.14836 |