Geometry & Topology Monographs, Vol. 4 (2002),
Invariants of knots and 3-manifolds (Kyoto 2001),
Paper no. 1, pages 1--12.

Bracelets and the Goussarov Filtration of the Space of Knots

Dror Bar-Natan

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.

Keywords. Bracelets, interdependent modifications, Goussarov, Vassiliev

AMS subject classification. Primary: 57M27.

E-print: arXiv:math.GT/0111267

Submitted to GT on 26 November 2001. (Revised 17 February 2002.) Paper accepted 22 July 2002. Paper published 19 September 2002.

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Dror Bar-Natan
Department of Mathematics, University of Toronto
Toronto Ontario M5S 3G3, Canada
Email: drorbn@math.toronto.edu
URL: http://www.math.toronto.edu/~drorbn
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