On finite type 3-manifold invariants IV: comparison of definitions

Source abstract

The present paper is a continuation of [ Ga ], [ GL1 ] and [ GO ]. Using a key lemma we compare two currently existing definitions of finite type invariants of oriented integral homology spheres and show that type 3 m invariants in the sense of Ohtsuki [ Oh ] are included in type m invariants in the sense of the first author [ Ga ]. This partially answers question 1 of [ Ga ]. We show that type 3 m invariants of integral homology spheres in the sense of Ohtsuki map to type 2 m invariants of knots in S 3 , thus answering question 2 from [ Ga ].