Year: 2025
Type: article
Abstract: We define a 1-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).
Source: Algebraic & Geometric Topology
Authors: Zhenkun Li, Yi Xie, Boyu Zhang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4411625186