On geometric realizations of the extreme Khovanov homology of pretzel links

Jinseok Oh; Mark H. Siggers; Seung Yeop Yang; Hongdae Yun

doi:10.1016/j.topol.2025.109360

On geometric realizations of the extreme Khovanov homology of pretzel links

Jinseok Oh, Mark H. Siggers, Seung Yeop Yang, Hongdae Yun

Kyungpook National University

Research output: Contribution to journal › Article › peer-review

Abstract

González-Meneses, Manchón, and Silvero showed that the (hypothetical) extreme Khovanov homology of a link diagram is isomorphic to the reduced (co)homology of the independence simplicial complex of its Lando graph. Przytycki and Silvero conjectured that the extreme Khovanov homology of any link diagram is torsion-free. In this paper, we investigate explicit geometric realizations of the real-extreme Khovanov homology of pretzel links. This gives further support for the conjecture.

Original language	English
Article number	109360
Journal	Topology and its Applications
DOIs	https://doi.org/10.1016/j.topol.2025.109360
State	Accepted/In press - 2025

Keywords

Geometric realization
Homotopy type
Khovanov homology
Pretzel link

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10.1016/j.topol.2025.109360

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title = "On geometric realizations of the extreme Khovanov homology of pretzel links",

abstract = "Gonz{\'a}lez-Meneses, Manch{\'o}n, and Silvero showed that the (hypothetical) extreme Khovanov homology of a link diagram is isomorphic to the reduced (co)homology of the independence simplicial complex of its Lando graph. Przytycki and Silvero conjectured that the extreme Khovanov homology of any link diagram is torsion-free. In this paper, we investigate explicit geometric realizations of the real-extreme Khovanov homology of pretzel links. This gives further support for the conjecture.",

keywords = "Geometric realization, Homotopy type, Khovanov homology, Pretzel link",

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AU - Oh, Jinseok

AU - Siggers, Mark H.

AU - Yang, Seung Yeop

AU - Yun, Hongdae

PY - 2025

Y1 - 2025

N2 - González-Meneses, Manchón, and Silvero showed that the (hypothetical) extreme Khovanov homology of a link diagram is isomorphic to the reduced (co)homology of the independence simplicial complex of its Lando graph. Przytycki and Silvero conjectured that the extreme Khovanov homology of any link diagram is torsion-free. In this paper, we investigate explicit geometric realizations of the real-extreme Khovanov homology of pretzel links. This gives further support for the conjecture.

AB - González-Meneses, Manchón, and Silvero showed that the (hypothetical) extreme Khovanov homology of a link diagram is isomorphic to the reduced (co)homology of the independence simplicial complex of its Lando graph. Przytycki and Silvero conjectured that the extreme Khovanov homology of any link diagram is torsion-free. In this paper, we investigate explicit geometric realizations of the real-extreme Khovanov homology of pretzel links. This gives further support for the conjecture.

KW - Geometric realization

KW - Homotopy type

KW - Khovanov homology

KW - Pretzel link

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U2 - 10.1016/j.topol.2025.109360

DO - 10.1016/j.topol.2025.109360

M3 - Article

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SN - 0166-8641

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 109360

ER -

On geometric realizations of the extreme Khovanov homology of pretzel links

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Keywords

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