The loop expansion of the Kontsevich integral, the null-move and S-equivalence |
| |
Authors: | Stavros Garoufalidis Lev Rozansky |
| |
Institution: | a School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA b Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USA |
| |
Abstract: | The Kontsevich integral of a knot is a graph-valued invariant which (when graded by the Vassiliev degree of graphs) is characterized by a universal property; namely it is a universal Vassiliev invariant of knots. We introduce a second grading of the Kontsevich integral, the Euler degree, and a geometric null-move on the set of knots. We explain the relation of the null-move to S-equivalence, and the relation to the Euler grading of the Kontsevich integral. The null-move leads in a natural way to the introduction of trivalent graphs with beads, and to a conjecture on a rational version of the Kontsevich integral, formulated by the second author and proven in Geom. Top 8 (2004) 115 (see also Kricker, preprint 2000, math/GT.0005284). |
| |
Keywords: | primary 57N10 secondary 57M25 |
本文献已被 ScienceDirect 等数据库收录! |
|