Cobordism maps in Khovanov homology and singular instanton homology I

Hayato Imori; Taketo Sano; Kouki Sato; Masaki Taniguchi

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arXiv · 2505.12095

Cobordism maps in Khovanov homology and singular instanton homology I

Hayato Imori·Taketo Sano·Kouki Sato·Masaki Taniguchi

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Abstract

Khovanov homology and singular instanton Floer homology are both functorial with respect to link cobordisms. Although the two homology groups are related by a spectral sequence, direct correspondence between the cobordism maps has not been rigorously established. In this paper, we define a cobordism map on the instanton cube complex as a filtered chain map, and prove that it recovers the cobordism maps both in Khovanov homology and singular instanton theory. In a sequel paper, we further extend this cobordism map to immersed cobordisms.

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Hayato Imori, Taketo Sano, Kouki Sato, Masaki Taniguchi. 2025-05-17. Cobordism maps in Khovanov homology and singular instanton homology I. https://arxiv.org/abs/2505.12095

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