Khovanov homology and equivariant surfaces

Maciej Borodzik; Irving Dai; Abhishek Mallick; Matthew Stoffregen

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arXiv · 2507.13642

Khovanov homology and equivariant surfaces

Maciej Borodzik·Irving Dai·Abhishek Mallick·Matthew Stoffregen

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Abstract

We introduce a refinement of Bar-Natan homology for involutive links, extending the work of Lobb-Watson and Sano. We construct a new suite of numerical invariants and derive bounds for the genus of equivariant cobordisms between strongly invertible knots. Our invariants show that the difference between the equivariant slice genus and isotopy-equivariant slice genus can be arbitrarily large, whereas previously these were not known to differ.

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Maciej Borodzik, Irving Dai, Abhishek Mallick, Matthew Stoffregen. 2025-07-18. Khovanov homology and equivariant surfaces. https://arxiv.org/abs/2507.13642

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