A 1-variable Knot Polynomial denoted
or
.
![\begin{displaymath}
{\mathcal L}_L(A)\equiv (-A^3)^{-w(L)}\left\langle{L}\right\rangle{},
\end{displaymath}](k_340.gif) |
(1) |
where
is the Bracket Polynomial and
is the Writhe of
. This Polynomial is invariant
under Ambient Isotopy, and relates Mirror Images by
![\begin{displaymath}
{\mathcal L}_{L^*}={\mathcal L}_L(A^{-1}).
\end{displaymath}](k_341.gif) |
(2) |
It is identical to the Jones Polynomial with the change of variable
![\begin{displaymath}
{\mathcal L}(t^{-1/4}) = V(t).
\end{displaymath}](k_342.gif) |
(3) |
The
Polynomial of the Mirror Image
is the same as for
but with
replaced by
.
References
Kauffman, L. H. Knots and Physics. Singapore: World Scientific, p. 33, 1991.
© 1996-9 Eric W. Weisstein
1999-05-26