An Extension of Khovanov Homology to Immersed Surface Cobordisms

Scott Carter; Benjamin Cooper; Mikhail Khovanov; Vyacheslav Krushkal

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arXiv · 2510.14760

An Extension of Khovanov Homology to Immersed Surface Cobordisms

Scott Carter·Benjamin Cooper·Mikhail Khovanov·Vyacheslav Krushkal

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Abstract

We show that an oriented surface in $\mathbb{R}^4$ containing double point singularities induces a map between the Khovanov homology groups of its boundary links in a functorial way. As part of this work, the movie moves of Carter and Saito are extended to surfaces with double points.

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Scott Carter, Benjamin Cooper, Mikhail Khovanov, Vyacheslav Krushkal. 2025-10-16. An Extension of Khovanov Homology to Immersed Surface Cobordisms. https://arxiv.org/abs/2510.14760

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