A whittled complex for the Khovanov homology of torus links
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912822897672192 |
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| author | Caprau, Carmen Gonzalez, Nicolle Lee, Christine Ruey Shan Sazdanovic, Radmila |
| author_facet | Caprau, Carmen Gonzalez, Nicolle Lee, Christine Ruey Shan Sazdanovic, Radmila |
| contents | We give an algorithm for reducing the number of generators of the Khovanov chain complex of the torus braid $ft^k_n = (σ_1σ_2\cdots σ_{n-1})^k$ on $n$ strands by applying Bar-Natan Gaussian elimination along a distinguished set of Gaussian elimination isomorphisms. We call the resulting complex $\mathcal{FT}^k_n$ a \emph{whittled complex} for the Khovanov homology of torus braids. Using this algorithm, we provide a bound for the number of generators at a fixed homological degree in our whittled complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09079 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A whittled complex for the Khovanov homology of torus links Caprau, Carmen Gonzalez, Nicolle Lee, Christine Ruey Shan Sazdanovic, Radmila Geometric Topology We give an algorithm for reducing the number of generators of the Khovanov chain complex of the torus braid $ft^k_n = (σ_1σ_2\cdots σ_{n-1})^k$ on $n$ strands by applying Bar-Natan Gaussian elimination along a distinguished set of Gaussian elimination isomorphisms. We call the resulting complex $\mathcal{FT}^k_n$ a \emph{whittled complex} for the Khovanov homology of torus braids. Using this algorithm, we provide a bound for the number of generators at a fixed homological degree in our whittled complex. |
| title | A whittled complex for the Khovanov homology of torus links |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2601.09079 |