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Title: The 3-loop polynomial of knots obtained by plumbing the doubles of two knots
Authors: YAMAGUCHI, Kouki
Issue Date: Jul-2022
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Start page: 1
End page: 48
Thesis number: RIMS-1963
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.
URI: http://hdl.handle.net/2433/275863
Related Link: http://www.kurims.kyoto-u.ac.jp/preprint/index.html
Appears in Collections:Research Institute for Mathematical Sciences, preprints

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