Abstract
In this paper, we define a polynomial invariant of regular isotopy, G L , for oriented knot and link diagrams L. From G L by multiplying it by a normalizing factor, we obtain an ambient isotopy invariant, N L , for oriented knots and links. We compare the polynomial N L with the original Jones polynomial and with the normalized bracket polynomial. We show that the polynomial N L yields the Jones polynomial and the normalized bracket polynomial. As examples, we give the polynomial G L of some knot and link diagrams and compute the polynomial G L for torus links of type (2, n), and applying computer algebra (MAPLE) techniques, we calculate the polynomial G L of torus links of type (2, n). Furthermore we give its applications to alternating links.
Published Version
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