A deformation of Asaeda-Przytycki-Sikora homology

Zhenkun Li; Yi Xie; Boyu Zhang

doi:10.2140/agt.2025.25.1545

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arXiv · 2302.11109

A deformation of Asaeda-Przytycki-Sikora homology

Zhenkun Li·Yi Xie·Boyu Zhang

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Abstract

We define a 1-parameter family of homology invariants for links in thickened oriented surfaces. It recovers the homology invariant of Asaeda-Przytycki-Sikora (arxiv:0409414) and the invariant defined by Winkeler (arxiv:2106.03834). 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 non-trivial 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 the main theorem of arxiv:2208.13963.

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Zhenkun Li, Yi Xie, Boyu Zhang. 2023-02-22. A deformation of Asaeda-Przytycki-Sikora homology. https://doi.org/10.2140/agt.2025.25.1545

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