ON FINITE-TYPE-3-MANIFOLD INVARIANTS - III - MANIFOLD WEIGHT SYSTEMS

The present paper is a continuation of [11,6] devoted io the study of finite type invariants of integral homology 3-spheres. We introduce th e notion of manifold weight systems, and show that type m invariants o f integral homology 3-spheres are determined (modulo invariants of typ e m-1) by their associated manifold weight systems. In particular, we deduce a vanishing theorem for finite type invariants. We show that th e space of manifold weight systems forms a commutative, co-commutative Hopf algebra and that the map from finite type invariants to manifold weight systems is an algebra map. We conclude with better bounds for the graded space of finite type invariants of integral homology 3-sphe res. (C) 1997 Elsevier Science Ltd. All rights reserved.