Vassiliev invariants as polynomials

Simon Willerton

Banach Center Publications (1998)

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

Abstract

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

How to cite

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Willerton, 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

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  1. [1] D. Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) no. 2, 423-472. Zbl0898.57001
  2. [2] D. Bar-Natan, Polynomial invariants are polynomial, Mathematical Research Letters, 2 (1995) 239-246. Zbl0851.57001
  3. [3] J. Birman and X. S. Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993), 225-270. Zbl0812.57011
  4. [4] U. Burri, For a fixed Turaev shadow all 'Jones-Vassiliev' invariants depend polynomially on the gleams, University of Basel preprint, March 1995. 
  5. [5] J. Dean, Many classical knot invariants are not Vassiliev invariants, J. Knot Theory Ramifications, 3 (1994) 7-9. Zbl0816.57009
  6. [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. [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. [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. [9] T. Stanford, Finite-type invariants of knots, links, and graphs, Topology 35 (1996) 1027-1050. Zbl0863.57005
  10. [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. [11] T. Stanford, Computing Vassiliev's invariants, University of California at Berkeley preprint, December 1995. 
  12. [12] R. Trapp, Twist sequences and Vassiliev invariants, J. Knot Theory Ramifications., 3 (1994) 391-405. Zbl0841.57019
  13. [13] V. A. Vassiliev, Complements of discriminants of smooth maps: topology and applications, Trans. of Math. Mono. 98, Amer. Math. Soc., Providence, 1992. 
  14. [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. [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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