Hopf algebras and invariants of 3-manifolds

Abstract

This paper studies invariants of 3-manifolds derived from finite dimensional Hopf algebras. The invariants are based on right integrals for the Hopf algebras. In fact, it is shown that the defining property of the right integral is an algebraic translation of a necessary condition for invariance under handle slides in the Kirby calculus. The resulting class of invariants is distinct from the class of Witten-Reshetikhin-Turaev invariants.