4-dimensional Skein modules, Handle attachments, and Tangles

Gage Martin; Mary Stelow; Mira Wattal

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arXiv · 2602.17825

4-dimensional Skein modules, Handle attachments, and Tangles

Gage Martin·Mary Stelow·Mira Wattal

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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 $S^3 \times I$ 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.

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Gage Martin, Mary Stelow, Mira Wattal. 2026-02-19. 4-dimensional Skein modules, Handle attachments, and Tangles. https://arxiv.org/abs/2602.17825

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