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This paper aims to refine Bar-Natan homology for involutive links and construct new numerical invariants.

July 13, 2026Advances in MathematicsOpen Access

Khovanov homology and equivariant surfaces

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This paper aims to refine Bar-Natan homology for involutive links and construct new numerical invariants.
Develop a refinement of Bar-Natan homology for involutive links.
Construct numerical invariants related to equivariant cobordisms.
Analyze the relationship between equivariant slice genus and isotopy-equivariant slice genus.
The new invariants indicate the difference between equivariant slice genus and isotopy-equivariant slice genus can be arbitrarily large.
Previously, it was not known that these two measurements could differ significantly.

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Randomized trial introduces new invariants for equivariant surface analysis, suggesting significant differences in genus measurements.

Borodzik et al. (2026) studied this question.

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