I have seen that usually one finds polynomial invariants for oriented links (for example the Jones polynomial, the Hompfly polynomial). Does anyone know what polynomial invariants exist for non-oriented links?
Thank you for the help.


**Update**
I have found out that there exists another polynomial, not mentioned in the other answers/comments. It is the *BLM/Ho polynomial*. One can read the definition in the original papers (Brandt, R. D.; Lickorish, W. B. R.; and Millett, K. C. "A Polynomial Invariant for Unoriented Knots and Links." Invent. Math. 84, 563-573, 1986; Ho, C. F. "A New Polynomial for Knots and Links--Preliminary Report." Abstracts Amer. Math. Soc. 6, 300, 1985) or <http://mathworld.wolfram.com/BLMHoPolynomial.html> 



Polynomial invariants for unoriented links
Colored Kauffman polynomials are independent of orientations of links. If you look at the skein relation of Kauffman polynomial, there is no arrow. This is true for colored cases. Kauffman polynomials are related to SO(N) quantum knot invariants by substitution $q^{N-1}=a$. Since the representations of SO(N) are pseudo-real, they are independent of orientation.


