Abstract

. Recently Ohtsuki [Oh2], motivated by the notion of finite type knot invariants, introduced the notion of finite type invariants for oriented, integral homology 3-spheres (ZHS for short). In the present paper we propose another definition of finite type invariants of ZHS and give equivalent reformulations of our notion. We show that our invariants form a filtered commutative algebra and are of finite type in in the sense of Ohtsuki and thus conclude that the associated graded algebra is a priori finite dimensional in each degree. We discover a new set of restrictions that Ohtsuki's invariants satisfy and give a set of axioms that characterize the Casson invariant. Finally, we pose a set of questions relating the finite type 3-manifold invariants with the (Vassiliev) knot invariants. Contents 1. Introduction 2 1.1. History 1.2. A review of Ohtsuki's definition 1.3. Variations for finite type 3-manifold invariants 1.4. Statement of the results 1.5. Plan of the proof 1.6. Acknowledgmen...

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