Frobenius Algebras, Factorization Homology and the Reshetikhin-Turaev Invariants

TL;DR

This paper constructs a diffeomorphism invariant vector in the skein module of closed 3-manifolds using factorization homology and Frobenius algebras, generalizing Reshetikhin-Turaev invariants.

Contribution

It introduces a new method to produce 3-manifold invariants via factorization homology with Frobenius algebras, extending Reshetikhin-Turaev invariants.

Findings

Constructs diffeomorphism invariant vectors in skein modules.

Recovers Reshetikhin-Turaev invariants as a special case.

Provides a framework linking Frobenius algebras and 3D topological invariants.

Abstract

For a ribbon fusion category $\mathcal{A}$ and a special symmetric commutative Frobenius algebra $F$ in $\mathcal{A}$, we use factorization homology and the ansular correlators obtained via the modular microcosm principle to construct a diffeomorphism invariant vector inside the skein module of any closed oriented three-dimensional manifold. If $\mathcal{A}$ is a modular fusion category and $F$ is the monoidal unit, this recovers the Reshetikhin-Turaev invariants.