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On the KBSM of links in lens spaces

Boštjan Gabrovšek

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

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

Corresponding author.

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and

Enrico Manfredi

Department of Mathematics, University of Bologna, Italy

E-mail Address: enrico.manfredi3@unibo.it

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https://doi.org/10.1142/S0218216518500062Cited by:1 (Source: Crossref)

Abstract

In this paper, the properties of the Kauffman bracket skein module (KBSM) of $L (p, q)$ are investigated. Links in lens spaces are represented both through band and disk diagrams. The possibility to transform between the diagrams enables us to compute the KBSM on an interesting class of examples consisting of inequivalent links with equivalent lifts in the $3$ -sphere. The computations show that the KBSM is an essential invariant, that is, it may take different values on links with equivalent lifts. We also show how the invariant is related to the Kauffman bracket of the lift in the $3$ -sphere.

Keywords:

AMSC: 57M25, 57M27, 57M10

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