Gropes and the rational lift of the Kontsevich integral
Tom 184 / 2004
Fundamenta Mathematicae 184 (2004), 73-77
MSC: Primary 57M27
DOI: 10.4064/fm184-0-5
Streszczenie
We calculate the leading term of the rational lift of the Kontsevich integral, $Z^{\mathfrak r\mathfrak a\mathfrak t}$, introduced by Garoufalidis and Kricker, on the boundary of an embedded grope of class ,$2n$. We observe that it lies in the subspace spanned by connected diagrams of Euler degree $2n-2$ and with a bead $t-1$ on a single edge. This places severe algebraic restrictions on the sort of knots that can bound gropes, and in particular implies the two main results of the author's thesis [1], at least over the rationals.
