An Extension of Khovanov Homology to Immersed Surface Cobordisms

Scott Carter; Benjamin Cooper; Mikhail Khovanov; Vyacheslav Krushkal

doi:10.48550/arxiv.2510.14760

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An Extension of Khovanov Homology to Immersed Surface Cobordisms

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An Extension of Khovanov Homology to Immersed Surface Cobordisms

Scott Carter, Benjamin Cooper, Mikhail Khovanov and Vyacheslav Krushkal

ArXiv.org

Cornell University

10/16/2025

DOI: 10.48550/arxiv.2510.14760

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We show that an oriented surface in R4 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.

Mathematics - Geometric Topology

Mathematics - Quantum Algebra

Details

Title: Subtitle: An Extension of Khovanov Homology to Immersed Surface Cobordisms
Creators: Scott Carter
Benjamin Cooper
Mikhail Khovanov
Vyacheslav Krushkal
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2510.14760
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 10/16/2025
Academic Unit: Mathematics
Record Identifier: 9985014805702771

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