Comparing finite type invariants of knots and integral homology 3-spheres

Abstract

Using elementary counting methods of weight systems for finite type invariants of knots and integral homology 3-spheres, in the spirit of [B-NG], we answer positively three questions raised in [Ga]. In particular, we exhibit a one-to-one map from the space of finite type invariants of integral homology 3-spheres to the space of finite type invariants of knots in $S^3$.