Spin Link Homology
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913409366228992 |
|---|---|
| author | Bodish, Elijah Elias, Ben Rose, David E. V. |
| author_facet | Bodish, Elijah Elias, Ben Rose, David E. V. |
| contents | We put a new spin on Khovanov--Rozansky homology. That is, we equip $Λ^n$-colored $\mathfrak{sl}_{2n}$ Khovanov--Rozansky homology with an involution whose $\pm 1$-eigenspaces are link invariants. When $n=1,2,3$ (and assuming technical conjectures for $n \geq 4$), we prove that this refined invariant categorifies the spin-colored $\mathfrak{so}_{2n+1}$ quantum link polynomial. Along the way, we partially develop the theory of quantum $\mathfrak{so}_{2n+1}$ webs and make contact with $ι$quantum groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00189 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spin Link Homology Bodish, Elijah Elias, Ben Rose, David E. V. Quantum Algebra Geometric Topology Representation Theory 57K18, 17B37, 18N25 We put a new spin on Khovanov--Rozansky homology. That is, we equip $Λ^n$-colored $\mathfrak{sl}_{2n}$ Khovanov--Rozansky homology with an involution whose $\pm 1$-eigenspaces are link invariants. When $n=1,2,3$ (and assuming technical conjectures for $n \geq 4$), we prove that this refined invariant categorifies the spin-colored $\mathfrak{so}_{2n+1}$ quantum link polynomial. Along the way, we partially develop the theory of quantum $\mathfrak{so}_{2n+1}$ webs and make contact with $ι$quantum groups. |
| title | Spin Link Homology |
| topic | Quantum Algebra Geometric Topology Representation Theory 57K18, 17B37, 18N25 |
| url | https://arxiv.org/abs/2407.00189 |