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

Altintaş I., TAŞKÖPRÜ K.

Turkish Journal of Mathematics, cilt.42, sa.2, ss.515-527, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1608-19
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.515-527
  • Anahtar Kelimeler: Alexander polynomial, Delta derivative, Derivative in group rings, Free derivative, Time scales
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

© 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.