|Title:||The 3-loop polynomial of knots obtained by plumbing the doubles of two knots|
|Publisher:||Research Institute for Mathematical Sciences, Kyoto University|
|Abstract:||The 3-loop polynomial of a knot is a polynomial presenting the 3-loop part of the Kontsevich invariant of knots. In this paper, we calculate the 3-loop polynomial of knots obtained by plumbing the doubles of two knots; this class of knots includes untwisted Whitehead doubles. We construct the 3-loop polynomial by calculating the rational version of the Aarhus integral of a surgery presentation. As a consequence, we obtain an explicit presentation of the 3-loop polynomial for the knots.|
|Appears in Collections:||Research Institute for Mathematical Sciences, preprints|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.