Khovanov-Rozansky homologies, Bott-Samelson spaces and twisted cohomology
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913491904888832 |
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| author | Mejia-Gomez, Tomas |
| author_facet | Mejia-Gomez, Tomas |
| contents | By means of Rasmussen's formulation of Khovanov-Rozansky homology originally given over $\mathbb{Q}$ in arXiv:math/0607544, we compare different flavors of $\mathfrak{sl}(n)$ link homology with the link invariants obtained by Kitchloo in arXiv:1910.07444 via twistings of Borel equivariant cohomology applied to the symmetry breaking spectra. In particular, we see how these geometric constructions based on Bott-Samelson varieties produce equivariant integral $\mathfrak{sl}(n)$ link homology with either specialized or universal potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02940 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Khovanov-Rozansky homologies, Bott-Samelson spaces and twisted cohomology Mejia-Gomez, Tomas Algebraic Topology Geometric Topology Quantum Algebra By means of Rasmussen's formulation of Khovanov-Rozansky homology originally given over $\mathbb{Q}$ in arXiv:math/0607544, we compare different flavors of $\mathfrak{sl}(n)$ link homology with the link invariants obtained by Kitchloo in arXiv:1910.07444 via twistings of Borel equivariant cohomology applied to the symmetry breaking spectra. In particular, we see how these geometric constructions based on Bott-Samelson varieties produce equivariant integral $\mathfrak{sl}(n)$ link homology with either specialized or universal potential. |
| title | Khovanov-Rozansky homologies, Bott-Samelson spaces and twisted cohomology |
| topic | Algebraic Topology Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2409.02940 |