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The modified Kontsevich invariant
The modified Kontsevich invariant and quantum invariants
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A(Sl algebraically split Borromean ring chord diagram component connected sum Corollary dashed chord dashed loop definition degree 3d Dehn surgery denote elementary quasi-tangle diagrams equal equivalence relation finite type invariants framed knots Hence Hopf algebra horizontal lines IHX relation integral homology 3-sphere invariant of 3-manifolds invariants of degree invariants of knots isotopy invariance Kd/Kd+i KII move Kirby moves knots and 3-manifolds Lie algebra linear map linear sum link diagram modified Kontsevich invariant modulo obtain the invariance obtain the required oriented framed link Pn+i power series Proof of Theorem properties Proposition 4.3 quantum G required formula right hand side show an example singular knot skein relation solid circle solid interval split and unit-framed STU relation sufficient to show sum of chord surjection tangle diagram Theorem 7.3 trivalent vertices trivial knot uni-trivalent graph universal perturbative invariant universal quantum invariant vanishes Vassiliev invariants vertex Wb,r weight system