I apologize for my idiot question but it just is not clear to me how skein relations with coefficient , A, of higher powers is useful? For higher powers of A = x^-1/2 - x^1/2 we have something like: A = (1 − x)/x^1/2 A^2 = (1 − 2x + x2)/x A^3 = (1 − x)^3 / x^3/2 = (1 − 3x + 3x2 − x3)/x^3/2 A^4 = (1 − x)^4 / x^2 = (1 − 4x + 6x2 − 4x3 + x4)/x^2
How are these useful and where are they used? In the wiki article on skein there is reference to higher dimensional analogs to skein. Is this what they are referring to?
Thanks for any replies!