On a theorem of Kontsevich.
Morita classes in the homology of automorphism groups of free groups.
Gropes and the rational lift of the Kontsevich integral
We calculate the leading term of the rational lift of the Kontsevich integral, , 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.
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