STATE-SUM INVARIANTS OF 4-MANIFOLDS

We provide, with proofs, a complete description of the authors' constr uction of state-sum invariants announced in [CY], and its generalizati on to an arbitrary (artinian) semisimple tortile category. We also dis cuss the relationship of these invariants to generalizations of Broda' s surgery invariants [Br1,Br2] using techniques developed in the case of the semi-simple sub-quotient of Rep(U-q(sl2)) (q a principal 4r(th) root of unity) by Roberts [Ro1]. We briefly discuss the generalizatio ns to invariants of 4-manifolds equipped with 2-dimensional (co)homolo gy classes introduced by Yetter [Y6] and Roberts [Ro2].