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The Alexander polynomial of links in lens spaces

E. Horvat

Faculty of Education, University of Ljubljana, Kardeljeva ploščad 16, SI-1000 Ljubljana, Slovenia

E-mail Address: eva.horvat@pef.uni-lj.si

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and

Boštjan Gabrovšek

Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

Faculty of Mechanical Engineering, Aškerčeva 6, SI-1000 Ljubljana, Slovenia

E-mail Address: bostjan.gabrovsek@fs.uni-lj.si

Corresponding author.

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https://doi.org/10.1142/S0218216519500494Cited by:2 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 57M25, 57M27

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