Skein lasagna modules for 2-handlebodies

TL;DR

This paper provides a new description and explicit calculations of the skein lasagna modules for certain 4-manifolds, extending the understanding of these invariants in low-handlebody cases.

Contribution

It offers an elementary diagrammatic description of skein lasagna modules for 4-manifolds without 1- and 3-handles, including explicit computations for disk bundles over S^2.

Findings

Explicit description of skein lasagna modules for specific 4-manifolds

Calculations for disk bundles over S^2

Extension of the theory to low-handlebody 4-manifolds

Abstract

Morrison, Walker, and Wedrich used the blob complex to construct a generalization of Khovanov-Rozansky homology to links in the boundary of a 4-manifold. The degree zero part of their theory, called the skein lasagna module, admits an elementary definition in terms of certain diagrams in the 4-manifold. We give a description of the skein lasagna module for 4-manifolds without 1- and 3-handles, and present some explicit calculations for disk bundles over $S^2$.