On the notion of Khovanov A-adequacy

Lizzie Buchanan; Huizheng Guo; Gabriel Montoya-Vega; Yongwu Rong; Marithania Silvero

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arXiv · 2502.17637

On the notion of Khovanov A-adequacy

Lizzie Buchanan·Huizheng Guo·Gabriel Montoya-Vega·Yongwu Rong·Marithania Silvero

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Abstract

The concept of adequate links, introduced by Lickorish and Thistlethwaite as a generalization of alternating links, has recently gained interest among knot theorists in the context of Khovanov homology. Przytycki and Silvero introduced the more general concept of Khovanov adequacy: a diagram is Khovanov-adequate if its associated Khovanov chain complexes at both potential maximal and minimal quantum gradings have non-trivial homology. This article explores Khovanov adequacy within the framework of independence complexes and the calculation of the homotopy type of extreme Khovanov spectra.

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Lizzie Buchanan, Huizheng Guo, Gabriel Montoya-Vega, Yongwu Rong, Marithania Silvero. 2025-02-24. On the notion of Khovanov A-adequacy. https://arxiv.org/abs/2502.17637

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