Invariants of 3-Manifolds Derived From Finite Dimensional Hopf Algebras

TL;DR

This paper introduces new invariants for 3-manifolds derived from finite-dimensional Hopf algebras, which differ from existing Witten-Reshetikhin-Turaev invariants, expanding the toolkit for 3-manifold topology.

Contribution

It constructs a novel class of 3-manifold invariants based on right integrals of finite-dimensional Hopf algebras, distinct from known quantum invariants.

Findings

New invariants are mathematically well-defined.

The invariants are proven to be different from Witten-Reshetikhin-Turaev invariants.

The approach broadens the understanding of algebraic structures in topology.

Abstract

This paper studies invariants of 3-manifolds derived from certain fin ite dimensional Hopf algebras. The invariants are based on right integrals for these algebras. It is shown that the resulting class of invariants is distinct from the class of Witten-Reshetikhin-Turaev invariants.