Gropes and the rational lift of the Kontsevich integral

Volume 184 / 2004

James Conant Fundamenta Mathematicae 184 (2004), 73-77 MSC: Primary 57M27 DOI: 10.4064/fm184-0-5


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.


  • James ConantDepartment of Mathematics
    University of Tennessee
    Knoxville, TN 37996-1300, U.S.A.

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