Conway skein equivalence
From Encyclopedia of Mathematics
An equivalence relation on the set of links in 
(cf. also Link). It is the smallest equivalence relation on ambient isotopy classes of oriented links, denoted by 
, that satisfies the following condition: If 
and 
are Conway skein triples (cf. also Conway skein triple) such that if 
and 
then 
, and, furthermore, if 
and 
then 
.
Skein equivalent links have the same Jones–Conway polynomials (cf. also Jones–Conway polynomial) and the same Murasugi signatures (for links with non-zero determinant, cf. also Signature). The last property generalizes to Tristram–Levine signatures.
References
| [a1] | J.H. Conway, "An enumeration of knots and links" J. Leech (ed.) , Computational Problems in Abstract Algebra , Pergamon (1969) pp. 329–358 |
| [a2] | C.A. Giller, "A family of links and the Conway calculus" Trans. Amer. Math. Soc. , 270 : 1 (1982) pp. 75–109 |
How to Cite This Entry:
Conway skein equivalence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conway_skein_equivalence&oldid=50173
Conway skein equivalence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conway_skein_equivalence&oldid=50173
This article was adapted from an original article by Jozef Przytycki (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article