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

Autor:	İsmet Altıntaş, Kemal Taşköprü
Přispěvatelé:	Altintas, I, Taskopru, K, Sakarya Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü, Altıntaş, İsmet
Rok vydání:	2018
Předmět:	Pure mathematics Generalization General Mathematics Time scales delta derivative derivative in group rings free derivative Alexander polynomial Alexander polynomial Delta derivative Mathematics::Geometric Topology Mathematics
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
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0633f42274823cb2c64073daff7f25de https://dergipark.org.tr/tr/pub/tbtkmath/issue/45644/574839 Zobrazit plný text záznamu