A generalization of the Alexander polynomial as an application of the delta derivative
Autor: | İsmet Altıntaş, Kemal Taşköprü |
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Přispěvatelé: | Altintas, I, Taskopru, K, Sakarya Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü, Altıntaş, İsmet |
Rok vydání: | 2018 |
Předmět: | |
Zdroj: | Volume: 42, Issue: 2 515-527 Turkish Journal of Mathematics |
ISSN: | 1300-0098 1303-6149 |
Popis: | 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. |
Databáze: | OpenAIRE |
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