The equality of 3-manifold invariants

TL;DR

This paper proves that the invariants of 3-manifolds derived from Kuperberg's involutory Hopf algebra approach and the authors' spherical Hopf algebra approach are equivalent when both are applicable, unifying two frameworks.

Contribution

It establishes the equality of two different 3-manifold invariants, bridging the gap between involutory and spherical Hopf algebra methods.

Findings

Invariants coincide for Hopf algebras where both are defined.

Unification of two approaches to 3-manifold invariants.

Provides a deeper understanding of the algebraic structures underlying 3-manifold invariants.

Abstract

The invariants of 3-manifolds defined by Kuperberg for involutory Hopf algebras and those defined by the authors for spherical Hopf algebras are the same for Hopf algebras on which they are both defined.