Skip to main content
Article thumbnail
Location of Repository

Finite Type Invariants of W-Knotted Objects: From Alexander to Kashiwara and Vergne (self-reference), paper and related files at nVassiliev [BN1] D. Bar-Natan, On the Vassiliev knot invariants, Topology 34

By Dror Bar-natan and Zsuzsanna Dancso


Abstract. w-Knots, and more generally, w-knotted objects (w-braids, w-tangles, etc.) make a class of knotted objects which is wider but weaker than their “usual ” counterparts. To get (say) w-knots from u-knots, one has to allow non-planar “virtual ” knot diagrams, hence enlarging the the base set of knots. But then one imposes a new relation, the “overcrossings commute ” relation, further beyond the ordinary collection of Reidemeister moves, making w-knotted objects a bit weaker once again. The group of w-braids was studied (under the name “welded braids”) by Fenn, Rimanyi and Rourke FennRimanyiRourke:BraidPermutation [FRR] and was shown to be isomorphic to the McCool group McCool:BasisConjugating [Mc] of “basisconjugating” automorphisms of a free group Fn — the smallest subgroup of Aut(Fn) that contains both braids and permutations. Brendle and Hatcher BrendleHatcher:RingsAndWickets [BH], in work that traces back to Goldsmith Goldsmith:MotionGroups [Gol], have shown this group to be a group of movies of flying rings in R3

Year: 1995
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.