1 1 O ct 2 00 4 Surgery on a single clasper and the 2 - loop part of the Kontsevich integral ∗
نویسنده
چکیده
We study the 2-loop part of the rational Kontsevich integral of a knot in an integer homology sphere. We give a general formula which explains how the 2-loop part of the Kontsevich integral of a knot changes after surgery on a single clasper whose leaves are not linked to the knot. As an application, we relate this formula with a conjecture of L. Rozansky about integrality of the 2-loop polynomial of a knot.
منابع مشابه
Surgery on a single clasper and the 2 - loop part of the Kontsevich integral ∗
We study the 2-loop part of the rational Kontsevich integral of a knot in an integer homology sphere. We give a general formula which explains how the 2-loop part of the Kontsevich integral of a knot changes after surgery on a single clasper whose leaves are not linked to the knot. As an application, we relate this formula with a conjecture of L. Rozansky about integrality of the 2-loop polynom...
متن کاملar X iv : m at h / 03 10 11 1 v 1 [ m at h . G T ] 8 O ct 2 00 3 On Kontsevich Integral of torus knots ∗
We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as a coloring of simple diagrams. We show that they behave under cyclic branched coverings in a very simple way. Our proof is combinatorial: it uses the results of Wheels and Wheelings and new decorations of diagrams.
متن کاملOn Knots with Trivial Alexander Polynomial
We use the 2-loop term of the Kontsevich integral to show that there are (many) knots with trivial Alexander polynomial which don’t have a Seifert surface whose genus equals the rank of the Seifert form. This is one of the first applications of the Kontsevich integral to intrinsically 3-dimensional questions in topology. Our examples contradict a lemma of Mike Freedman, and we explain what went...
متن کاملO ct 2 00 3 On Kontsevich Integral of torus knots ∗
We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as colorings of simple diagrams. We show that they behave under cyclic branched coverings in a very simple way. Our proof is combinatorial: it uses the results of Wheels and Wheelings and new decorations of diagrams.
متن کاملar X iv : d g - ga / 9 71 00 01 v 1 2 O ct 1 99 7 INTEGRAL INVARIANTS OF 3 - MANIFOLDS
This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer [2] and those of Kontsevich [9].
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تاریخ انتشار 2008