Cobordism maps in Khovanov homology and singular instanton homology I

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Hauptverfasser: Imori, Hayato, Sano, Taketo, Sato, Kouki, Taniguchi, Masaki
Format: Preprint
Veröffentlicht: 2025
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author Imori, Hayato
Sano, Taketo
Sato, Kouki
Taniguchi, Masaki
author_facet Imori, Hayato
Sano, Taketo
Sato, Kouki
Taniguchi, Masaki
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_12095
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Cobordism maps in Khovanov homology and singular instanton homology I
Imori, Hayato
Sano, Taketo
Sato, Kouki
Taniguchi, Masaki
Geometric Topology
57K18 57R58
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.
title Cobordism maps in Khovanov homology and singular instanton homology I
topic Geometric Topology
57K18 57R58
url https://arxiv.org/abs/2505.12095