Invariants of 3-manifolds from Hopf algebras

I will review my old result that one can build a "word" (or tensor network) in the Hopf PROP from a 3-manifold, to obtain a natural variation of the most standard quantum invariants of 3-manifolds. In the involutory case, one can go in the opposite direction and build a 3-manifold from a Hopf tensor network. This converse direction leads to a full solution of the Hopf word problem in principle, although not yet in practice.