Alexandrov polinom

V članku je razvit način za ločevanje med vozli različnih tipov. Na kratko je ponovljeno potrebno predznanje o predstavitvah grup in Tietzejevih transformacijah. Opisan je postopek za konstrukcijo Wirtingerjeve predstavitve grupe vozla iz diagrama vozla. S pomočja odvajanja v grupnem kolobarju so definirane invariante tipa vozla – elementarni ideali in vozelni polinomi. Njihova uporaba je prikazana na primerih.

Alexander polynomial

The main object of this article is to develop a way to distinguish among knots of different types. Some basic knowledge regarding presentations of groups and Tietze transformations is briefly recalled. A procedure of constructing the Wirtinger presentation of a knot group using the knot diagram is developed. Invariants of a knot type are defined with the use of derivation in a group ring – these are elementary ideals and knot polynomials. Their application is demonstrated in some examples.