Bracelets and the Goussarov Filtration of the Space of Knots
arXiv:math/0111267
Abstract
Following Goussarov's paper `Interdependent Modifications of Links and Invariants of Finite Degree' [Topology 37 (1998) 595--602] we describe an alternative finite type theory of knots. While (as shown by Goussarov) the alternative theory turns out to be equivalent to the standard one, it nevertheless has its own share of intrinsic beauty.
Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper1.abs.html