Finite Groups, Spherical 2-Categories, and 4-Manifold Invariants

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

In this paper we define a class of state-sum invariants of compact closed oriented piece-wise linear 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 [32], although it requires a slight generalization of that construction. We show that the state-sum invariant...

Spherical 2-categories and 4-manifold Invariants

m at h . Q A ] 2 3 M ay 1 99 8 Spherical 2 - categories and 4 - manifold invariants

m at h . Q A ] 2 5 O ct 1 99 8 Spherical 2 - categories and 4 - manifold invariants

On Finite Type 3-manifold Invariants Iii: Manifold Weight Systems

The present paper is a continuation of [Oh2] and [GL] devoted to the study of finite type invariants of integral homology 3-spheres. We introduce the notion of manifold weight systems, and show that type m invariants of integral homology 3-spheres are determined (modulo invariants of type m − 1) by their associated manifold weight systems. In particular we deduce a vanishing theorem for finite ...