Invariants of surfaces in smooth 4-manifolds from link homology
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912943451406336 |
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| author | Morrison, Kim Walker, Kevin Wedrich, Paul |
| author_facet | Morrison, Kim Walker, Kevin Wedrich, Paul |
| contents | We construct analogs of Khovanov-Jacobsson classes and the Rasmussen invariant for links in the boundary of any smooth oriented 4-manifold. The main tools are skein lasagna modules based on equivariant and deformed versions of $\mathfrak{gl}_N$ link homology, for which we prove non-vanishing and decomposition results. Along the way, we characterize precise technical conditions that allow a link homology theory to extend to skein lasagna 4-manifold invariants, we establish a decomposition theorem for deformed $\mathfrak{gl}_N$ skein lasagna modules, and we illustrate how Hopf link homology classes can be used to extend the functoriality of link homology theories to immersed link cobordisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariants of surfaces in smooth 4-manifolds from link homology Morrison, Kim Walker, Kevin Wedrich, Paul Geometric Topology Quantum Algebra We construct analogs of Khovanov-Jacobsson classes and the Rasmussen invariant for links in the boundary of any smooth oriented 4-manifold. The main tools are skein lasagna modules based on equivariant and deformed versions of $\mathfrak{gl}_N$ link homology, for which we prove non-vanishing and decomposition results. Along the way, we characterize precise technical conditions that allow a link homology theory to extend to skein lasagna 4-manifold invariants, we establish a decomposition theorem for deformed $\mathfrak{gl}_N$ skein lasagna modules, and we illustrate how Hopf link homology classes can be used to extend the functoriality of link homology theories to immersed link cobordisms. |
| title | Invariants of surfaces in smooth 4-manifolds from link homology |
| topic | Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2401.06600 |