# Vassiliev invariants as polynomials

Banach Center Publications (1998)

- Volume: 42, Issue: 1, page 457-463
- ISSN: 0137-6934

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topWillerton, Simon. "Vassiliev invariants as polynomials." Banach Center Publications 42.1 (1998): 457-463. <http://eudml.org/doc/208823>.

@article{Willerton1998,

abstract = {Three results are shown which demonstrate how Vassiliev invariants behave like polynomials.},

author = {Willerton, Simon},

journal = {Banach Center Publications},

keywords = {twist sequence; integration of weight systems; Leibniz rule; Vassiliev invariant},

language = {eng},

number = {1},

pages = {457-463},

title = {Vassiliev invariants as polynomials},

url = {http://eudml.org/doc/208823},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Willerton, Simon

TI - Vassiliev invariants as polynomials

JO - Banach Center Publications

PY - 1998

VL - 42

IS - 1

SP - 457

EP - 463

AB - Three results are shown which demonstrate how Vassiliev invariants behave like polynomials.

LA - eng

KW - twist sequence; integration of weight systems; Leibniz rule; Vassiliev invariant

UR - http://eudml.org/doc/208823

ER -

## References

top- [1] D. Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) no. 2, 423-472. Zbl0898.57001
- [2] D. Bar-Natan, Polynomial invariants are polynomial, Mathematical Research Letters, 2 (1995) 239-246. Zbl0851.57001
- [3] J. Birman and X. S. Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993), 225-270. Zbl0812.57011
- [4] U. Burri, For a fixed Turaev shadow all 'Jones-Vassiliev' invariants depend polynomially on the gleams, University of Basel preprint, March 1995.
- [5] J. Dean, Many classical knot invariants are not Vassiliev invariants, J. Knot Theory Ramifications, 3 (1994) 7-9. Zbl0816.57009
- [6] M. Domergue and P. Donato, Integrating a weight system of order n to an invariant of (n-1)-singular knots, J. Knot Theory Ramifications, 5 (1996) 23-35. Zbl0868.57010
- [7] M. Gussarov, On n-equivalence of knots and invariants of finite degree, in Topology of manifolds and varieties (O. Viro, editor), Amer. Math. Soc., Providence 1994, 173-192. Zbl0865.57007
- [8] J. H. Przytycki, Vassiliev-Gusarov skein modules of 3-manifolds and criteria for periodicity of knots, Proceedings of low-dimensional topology, May 18-23 1992, International Press, Cambridge MA, 1994.
- [9] T. Stanford, Finite-type invariants of knots, links, and graphs, Topology 35 (1996) 1027-1050. Zbl0863.57005
- [10] T. Stanford, The functoriality of Vassiliev-type invariants of links, braids, and knotted graphs, J. Knot Theory Ramifications, 3 (1994) 247-262. Zbl0841.57018
- [11] T. Stanford, Computing Vassiliev's invariants, University of California at Berkeley preprint, December 1995.
- [12] R. Trapp, Twist sequences and Vassiliev invariants, J. Knot Theory Ramifications., 3 (1994) 391-405. Zbl0841.57019
- [13] V. A. Vassiliev, Complements of discriminants of smooth maps: topology and applications, Trans. of Math. Mono. 98, Amer. Math. Soc., Providence, 1992.
- [14] S. Willerton, Vassiliev knot invariants and the Hopf algebra of chord diagrams, Math. Proc. Camb. Phil. Soc., 119 (1996) 55-65. Zbl0878.57013
- [15] S. Willerton, A combinatorial half-integration from weight system to Vassiliev knot invariant, J. Knot Theory Ramifications, to appear. Zbl0905.57005

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