Surgery on a single clasper and the 2-loop part of the Kontsevich integral

Details Surgery on a single clasper and the 2-loop part of the Kontsevich integral Surgery on a single clasper and the 2-loop part of the Kontsevich integral

2004-10-11

arxiv.org/abs/math/0410272v1

Mathematics

Geometric Topology

15 pages, 9 figures

Scientific paper

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.

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