Invariants of 3-Manifolds Derived From Finite Dimensional Hopf Algebras

This paper studies invariants of 3-manifolds derived from certain finite dimensional Hopf algebras via regular isotopy invariants of unoriented links in the blackboard framing. The invariants are based on right integrals for these Hopf algebras. It is shown that the resulting class of invariants is definitely distinct from the class of Witten-Reshetikhin-Turaev invariants. The invariant associated with the quantum double of a finite group G is treated in this context, and is shown to count the number of homomorphisms of the fundamental group of the 3-manifold to the given finite group G.