# Invariants of links of Conway type

@article{Przytycki1988InvariantsOL, title={Invariants of links of Conway type}, author={J{\'o}zef H. Przytycki and Paweł Traczyk}, journal={arXiv: Geometric Topology}, year={1988} }

The purpose of this paper is to present a certain combinatorial method of constructing invariants of isotopy classes of oriented tame links. This arises as a generalization of the known polynomial invariants of Conway and Jones. These invariants have one striking common feature. If L+, L- and L0 are diagrams of oriented links which are identical, except near one crossing point (as in Conway or Jones polynomials), then an invariant w(L) has the property: w(L+) is uniquely determined by w(L-) and…

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## References

SHOWING 1-10 OF 12 REFERENCES

On the Jones polynomial of closed 3-braids

- Mathematics
- 1985

In [J, 2] Vaughan Jones introduced a new polynomial VL(t ) which is an invariant of the isotopy type of an oriented knot or link L c S 3. The polynomial can be computed from an arbitrary…

A polynomial invariant for knots via von Neumann algebras

- Mathematics
- 1985

Thus, the trivial link with n components is represented by the pair (l ,n), and the unknot is represented by (si$2 * * • s n i , n) for any n, where si, $2, • • • > sn_i are the usual generators for…

On closed 3-braids, Memoirs AMS 151 1974

Combinatorics and knot theory

- Contemporary Mathematics,
- 1983