Two applications of elementary knot theory to Lie algebras and Vassiliev invariants

Details Two applications of elementary knot theory to Lie algebras and Vassiliev invariants Two applications of elementary knot theory to Lie algebras and Vassiliev invariants

2002-04-25

arxiv.org/abs/math/0204311v3

Geom. Topol. 7(2003) 1-31

Mathematics

Quantum Algebra

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper1.abs.html

Scientific paper

Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Wheels and Wheeling conjectures of [Bar-Natan, Garoufalidis, Rozansky and Thurston, arXiv:q-alg/9703025] and [Deligne, letter to Bar-Natan, January 1996, http://www.ma.huji.ac.il/~drorbn/Deligne/], which give, respectively, the exact Kontsevich integral of the unknot and a map intertwining two natural products on a space of diagrams. It turns out that the Wheeling map is given by the Kontsevich integral of a cut Hopf link (a bead on a wire), and its intertwining property is analogous to the computation of 1+1=2 on an abacus. The Wheels conjecture is proved from the fact that the k-fold connected cover of the unknot is the unknot for all k. Along the way, we find a formula for the invariant of the general (k,l) cable of a knot. Our results can also be interpreted as a new proof of the multiplicativity of the Duflo-Kirillov map S(g)-->U(g) for metrized Lie (super-)algebras g.

Affiliated with

Also associated with

No associations

Rating

Two applications of elementary knot theory to Lie algebras and Vassiliev invariants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Two applications of elementary knot theory to Lie algebras and Vassiliev invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two applications of elementary knot theory to Lie algebras and Vassiliev invariants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-98817