A whittled complex for the Khovanov homology of torus links

Carmen Caprau; Nicolle Gonzalez; Christine Ruey Shan Lee; Radmila Sazdanovic

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arXiv · 2601.09079

A whittled complex for the Khovanov homology of torus links

Carmen Caprau·Nicolle Gonzalez·Christine Ruey Shan Lee·Radmila Sazdanovic

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Abstract

We give an algorithm for reducing the number of generators of the Khovanov chain complex of the torus braid $ft^k_n = (\sigma_1\sigma_2\cdots \sigma_{n-1})^k$ 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.

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Carmen Caprau, Nicolle Gonzalez, Christine Ruey Shan Lee, Radmila Sazdanovic. 2026-01-14. A whittled complex for the Khovanov homology of torus links. https://arxiv.org/abs/2601.09079

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