Insensitivity of Khovanov homology under rim surgery

Qiuyu Ren; Fang-Rong Zhan

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arXiv · 2607.25302

Insensitivity of Khovanov homology under rim surgery

Qiuyu Ren·Fang-Rong Zhan

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Abstract

We show that rim surgery on a smooth, oriented, properly embedded surface in $B^4$ does not change the map on Khovanov homology induced by the surface, answering a question raised by Hayden and Sundber. More generally, the same insensitivity holds for a class of local surgery operations that we call local annulus replacements. Combined with the work of Hayden--Sundberg, this result yields exotic pairs of surfaces in $B^4$ that cannot be related by any sequence of local annulus replacements. We give two proofs, both making essential use of Khovanov skein lasagna modules.

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Qiuyu Ren, Fang-Rong Zhan. 2026-07-28. Insensitivity of Khovanov homology under rim surgery. https://arxiv.org/abs/2607.25302

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