The Alexander polynomial of links in lens spaces

Horvat, Eva (author), Gabrovšek, Boštjan (author)

We show how the Alexander polynomial of links in lens spaces is related to the classical Alexander polynomial of a link in the 3-sphere, obtained by cutting out the exceptional lens space fiber. It follows from this relationship that a certain normalization of the Alexander polynomial satisfies a skein relation in lens spaces.

• Language: English
• Keywords: links in lens spaces, links in 3-manifolds, Alexander polynomial, skein relation
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Year: 2019
• Number of pages: Str. 1-28
• Numbering: Vol. 28, no. 8
• PID: 20.500.12556/RUL-116713
• UDC: 515.162
• ISSN on article: 0218-2165
• DOI: 10.1142/S0218216519500494
• COBISS.SI-ID: 18686041
• Publication date in RUL: 05.06.2020

Record is a part of a journal

• Title: Journal of knot theory and its ramifications
• Shortened title: J. knot theory ramif.
• Publisher: World Scientific
• ISSN: 0218-2165
• COBISS.SI-ID: 3996249

Secondary language

• Language: Slovenian
• Title: O Aleksandrovem polinomu spletov v lečastih prostorih

Abstract

Pokažemo, kako je Aleksandrov polinom spletov v lečastih prostorih povezan s klasičnim Aleksandrovim polinomom spleta v 3-sferi, ki ga dobimo, če izrežemo izjemno vlakno lečastega prostora. Iz te povezave sledi, da normalizacija Aleksandrovega polinoma v lečastem prostoru ustreza premenjalni relaciji.