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A
deformation of Asaeda–Przytycki–Sikora homology
Zhenkun Li, Yi Xie and Boyu Zhang |
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Algebraic & Geometric Topology 25 (2025) 1545–1560
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Abstract |
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We define a -parameter family of homology invariants for links in thickened oriented surfaces. It recovers the homology invariant of Asaeda, Przytycki and Sikora (Algebr. Geom. Topol. 4 (2004) 1177–1210) and the invariant defined by Winkeler (Michigan Math. J. 74 (2024) 1–31). The new invariant can be regarded as a deformation of Asaeda–Przytycki–Sikora homology; it is not a Lee-type deformation as the deformation is only nontrivial when the surface is not simply connected. Our construction is motivated by computations in singular instanton Floer homology. We also prove a detection property for the new invariant, which is a stronger result than our previous work (Selecta Math. 29 (2023) art. id. 84). |
Keywords
homology theories in knot theory
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Mathematical Subject Classification
Primary: 57K18
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References |
Publication
Received: 9 March 2023
Revised: 8 November 2023
Accepted: 5 December 2023
Published: 20 June 2025
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Authors |
| Zhenkun Li | |
| School of Mathematics and
Statistics University of South Florida Tampa, FL United States |
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| Yi Xie | |
| Beijing International Center for
Mathematical Research Peking University Beijing China |
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| Boyu Zhang | |
| Department of Mathematics University of Maryland at College Park College Park, MD United States |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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