4-dimensional Skein modules, Handle attachments, and Tangles
Geometric Topology
2026-02-23 v1 Quantum Algebra
Abstract
Skein lasagna modules are a recent tool developed for the study of 4-manifolds. We provide general formula for 1-, 2-, and 3-handle attachments for skein modules defined with any functorial link theory in generalizing existing formula of Chen, Manolescu-Neithalath, Manolescu-Walker-Wedrich, and Ren-Willis. These formula are derived from a complete description of the gluing homomorphism on skein modules. For this description, we introduce a variation of these skein modules in the presence of distinguished 3-manifolds in the boundary. A similar construction was recently introduced independently by Blackwell-Krushkal-Luo.
Cite
@article{arxiv.2602.17825,
title = {4-dimensional Skein modules, Handle attachments, and Tangles},
author = {Gage Martin and Mary Stelow and Mira Wattal},
journal= {arXiv preprint arXiv:2602.17825},
year = {2026}
}