Year: 2026
Type: preprint
Abstract: We construct skein theory for 3-manifolds with embedded line defects, starting from the data of a ribbon tensor category and its balanced braided module category. We focus on line defects arising from quantum symmetric pairs, and prove finiteness properties for their defect skein modules. As an application, we consider $\mathbf{Z}_2$-equivariant skein theory and establish an equivalence with defect skein theory in certain settings, leading to a skein theoretical construction of a family of $\mathrm{C}^\vee\mathrm{C}$ DAHA-modules in the Type AIII case.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213501013