A topological model for the HOMFLY-PT polynomial
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917132526157824 |
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| author | Anghel, Cristina Ana-Maria Lee, Christine Ruey Shan |
| author_facet | Anghel, Cristina Ana-Maria Lee, Christine Ruey Shan |
| contents | We give the first known topological model for the HOMFLY-PT polynomial constructed directly from link diagrams. More precisely, we prove that this invariant is given by graded intersections between explicit Lagrangian submanifolds in a fixed configuration space on a Heegaard surface for the link exterior. The submanifolds are supported on a collection of arcs and ovals on the Heegaard surface. We also obtain two topological models for the Jones polynomial via a Heegaard surface associated to a link diagram. This opens up new avenues for constructing categorifications for the Jones and the HOMFLY-PT polynomials of a geometric nature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03679 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A topological model for the HOMFLY-PT polynomial Anghel, Cristina Ana-Maria Lee, Christine Ruey Shan Geometric Topology Algebraic Topology We give the first known topological model for the HOMFLY-PT polynomial constructed directly from link diagrams. More precisely, we prove that this invariant is given by graded intersections between explicit Lagrangian submanifolds in a fixed configuration space on a Heegaard surface for the link exterior. The submanifolds are supported on a collection of arcs and ovals on the Heegaard surface. We also obtain two topological models for the Jones polynomial via a Heegaard surface associated to a link diagram. This opens up new avenues for constructing categorifications for the Jones and the HOMFLY-PT polynomials of a geometric nature. |
| title | A topological model for the HOMFLY-PT polynomial |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2405.03679 |