Link homology and Frobenius extensions II

TL;DR

This paper develops a diagrammatic framework for Frobenius extensions in equivariant SL(2) link homology, clarifying foundational structures and proposing a flexible setup over non-degenerate rings, with applications to evaluations of seamed surfaces.

Contribution

It introduces a new diagrammatic scheme for Frobenius extensions in equivariant SL(2) link homology and extends the theory to work over broader base rings.

Findings

Provides a diagrammatic calculus for Frobenius extensions

Clarifies the structure of equivariant SL(2) link homology

Derives evaluations for seamed surfaces

Abstract

The first two sections of the paper provide a convenient scheme and additional diagrammatics for working with Frobenius extensions responsible for key flavors of equivariant SL(2) link homology theories. The goal is to clarify some basic structures in the theory and propose a setup to work over sufficiently non-degenerate base rings. The third section works out two related SL(2) evaluations for seamed surfaces.