An Extension of Khovanov Homology to Immersed Surface Cobordisms

2025/10/16 by Carter, Scott, Cooper, Benjamin, Khovanov, Mikhail +1
#FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2510.14760

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.

Citations

• Khovanov skein lasagna modules with 1-dimensional inputs
• Khovanov homology and exotic 4-manifolds
• Invariants of surfaces in smooth 4-manifolds from link homology
• Movie moves for framed foams from multijet transversality
• On the four-term relation on Khovanov homology
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• Decomposition of the first Vassiliev derivative of Khovanov homology and\n its application
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• Khovanov homology and the slice genus

Related

• Khovanov homology and exotic surfaces in the 4-ball
• Khovanov homology and cobordisms between split links
• Homotopical Khovanov homology
• Cobordism maps in Khovanov homology and singular instanton homology II
• A new computational tool for Khovanov cobordism maps