Colored sl(N) homology and SU(N) representations
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866908455023935488 |
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| author | Wang, Joshua |
| author_facet | Wang, Joshua |
| contents | We provide the first complete computations of colored sl(N) homology for a nontrivial knot. In doing so, we show that the colored sl(N) homology of the trefoil labeled by an exterior power of the defining representation is isomorphic to the cohomology of a closed manifold naturally associated to the trefoil. This manifold is the set of homomorphisms from the fundamental group of the complement of the trefoil to SU(N) that send meridians to a particular conjugacy class depending on the label. We also provide complete computations and analogous isomorphisms for the first nontrivial link, the Hopf link. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08409 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Colored sl(N) homology and SU(N) representations Wang, Joshua Geometric Topology Quantum Algebra We provide the first complete computations of colored sl(N) homology for a nontrivial knot. In doing so, we show that the colored sl(N) homology of the trefoil labeled by an exterior power of the defining representation is isomorphic to the cohomology of a closed manifold naturally associated to the trefoil. This manifold is the set of homomorphisms from the fundamental group of the complement of the trefoil to SU(N) that send meridians to a particular conjugacy class depending on the label. We also provide complete computations and analogous isomorphisms for the first nontrivial link, the Hopf link. |
| title | Colored sl(N) homology and SU(N) representations |
| topic | Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2211.08409 |