Finite-type invariants of classical and virtual knots

Topology

Volumn 39, Issue 5, 2000, Pages 1045-1068

  Goussarov, Mikhail ^a   Polyak, Michael ^b   Viro, Oleg ^a,c  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b TEL AVIV UNIVERSITY   (Israel)

^c UPPSALA UNIVERSITY   (Sweden)

Author keywords

Finite type invariants; Gauss diagrams; Virtual knots

Indexed keywords

EID: 0034259226     PISSN: 00409383     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0040-9383(99)00054-3     Document Type: Article

References (9)

1. D. Bar-Natan, Polynomial Invariants Are Polynomial, Harvard University Preprint, December 1994.
2. G. Cairns, D.M. Elton, The planarity problem for signed Gauss words, J. Knot Theory Ramifications 2 (1993) 359-367.
3. D. Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algeb. 23 (1982) 37-65.
4. L. Kauffman, Virtual Knot, Talks at MSRI Meeting in January 1997 and AMS Meeting at University of Maryland, College Park in March 1997.
5. L. Kauffman, Virtual knots theory, Eur. J. Combin., to appear, math.GT/9811028, preprint.
6. O.-P. Östlund, Preprint Uppsala University, 1997.
7. M. Polyak, O. Viro, Gauss diagram formulas for Vassiliev invariants, Int. Math. Res. Notices 11 (1994) 445-453.
8. M. Polyak, On the algebra of arrow diagrams, preprint 1998, available on the web from http:// www.math.tau.ac.il/ ~ polyak.
9. V.A. Vassiliev, Cohomology of knot spaces, in: V.I. Arnold (Ed.), Theory of Singularities and its Applications, Providence, Amer. Math. Soc., Providence, RI, 1990.