Higher representations and cornered Heegaard Floer homology
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866914195939786752 |
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| author | Manion, Andrew Rouquier, Raphael |
| author_facet | Manion, Andrew Rouquier, Raphael |
| contents | We develop the 2-representation theory of the odd one-dimensional super Lie algebra $gl(1|1)^+$ and show it controls the Heegaard-Floer theory of surfaces of Lipshitz, Ozsváth and Thurston. Our main tool is the construction of a tensor product for 2-representations. We show it corresponds to a gluing operation for surfaces, or the chord diagrams of arc decompositions. This provides an extension of Heegaard-Floer theory to dimension one, expanding the work of Douglas, Lipshitz and Manolescu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_09627 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Higher representations and cornered Heegaard Floer homology Manion, Andrew Rouquier, Raphael Representation Theory Geometric Topology Quantum Algebra We develop the 2-representation theory of the odd one-dimensional super Lie algebra $gl(1|1)^+$ and show it controls the Heegaard-Floer theory of surfaces of Lipshitz, Ozsváth and Thurston. Our main tool is the construction of a tensor product for 2-representations. We show it corresponds to a gluing operation for surfaces, or the chord diagrams of arc decompositions. This provides an extension of Heegaard-Floer theory to dimension one, expanding the work of Douglas, Lipshitz and Manolescu. |
| title | Higher representations and cornered Heegaard Floer homology |
| topic | Representation Theory Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2009.09627 |