A generalization of the Alexander polynomial as an application of the delta derivative
Turkish Journal of Mathematics, vol.42, no.2, pp.515-527, 2018 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 42 Issue: 2
- Publication Date: 2018
- Doi Number: 10.3906/mat-1608-19
- Journal Name: Turkish Journal of Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.515-527
- Keywords: Alexander polynomial, Delta derivative, Derivative in group rings, Free derivative, Time scales
- Bilecik Şeyh Edebali University Affiliated: Yes
Abstract
© Tübi˙tak.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.