A generalization of the Alexander polynomial as an application of the delta derivative

Authors : Ismet Altintaş, Kemal Taşköprü

Pages : 515-527

View : 8 | Download : 4

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :In this paper, we define the delta derivative in the integer group ring and we show that the delta derivative is well defined on the free groups. We also define a polynomial invariant of oriented knot and link by carrying the delta derivative to the link group. Since the delta derivative is a generalization of the free derivative, this polynomial invariant called the delta polynomial is a generalization of the Alexander polynomial. In addition, we present a new polynomial called the difference polynomial of oriented knot and link, which is similar to the Alexander polynomial and is a special case of the delta polynomial.
Keywords : Time scales, delta derivative, derivative in group rings, free derivative, Alexander polynomial