Finite groups, spherical 2-categories, and 4-manifold invariants

In this paper we dc line a class of state-sum invariants of closed oriented piece wise lineal 4-manifolds using finite groups. The definition of these state-sums Follows from the general abstract construction of 4-manifold invariants using spherical 2-categories. as we defined in an earlier paper. We show that the state survival invariants of Birmingham and Ratowski, who Studied Dijkgraaf Witten type invariants in dimension 3, are special examples of the general construction that we present in this paper. They showed that their invariants are non-trivial by some explicit computations, so our construction includes interesting examples already. Finally, wt indicate how our construction is related to homotopy 3-types. This connection suggests that there ale many more interesting examples of our construction to be found in the work on homotopy 3-types, by Brown, For example. (C) 2000 Academic press.