End Khovanov homology and exotic Lagrangian planes

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This is a Quantitative Study study.

Yanmei Teng

doi:10.48550/arxiv.2510.01151

October 1, 2025Open Access

End Khovanov homology and exotic Lagrangian planes

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Key Points

End khovanov homology serves as an invariant for surfaces in 4-space, and identifies exotic lagrangian planes.
The first instances of exotic lagrangian and symplectic planes in 4-space have been established using this new invariant.
This work broadens the understanding of the relationship between khovanov homology and differential topology.
The application of this invariant underscores its potential significance in studying ambient diffeomorphism classes.

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Implication

This paper defines the end khovanov homology as an invariant of surfaces, highlighting exotic lagrangian planes in 4-space.

Abstract

In this paper, we define the end Khovanov homology, which is an invariant of properly embedded surfaces in 4-space up to ambient diffeomorphism. Moreover, we apply this invariant to detect the first known examples of exotic Lagrangian and symplectic planes in 4-space.

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Yanmei Teng (2025) studied this question.

synapsesocial.com/papers/68e2537cd6d66a53c2474457 https://doi.org/10.48550/arxiv.2510.01151

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End Khovanov homology and exotic Lagrangian planes

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End Khovanov homology and exotic Lagrangian planes

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