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An important step for the computation of the HOMFLYPT skein module of the lens spaces $L (p, 1)$ via braids

International College Beijing, China Agricultural University, No. 17 Qinghua East Road, Haidian District, Beijing, 100083, P. R. China

E-mail Address: ioannis.diamantis@hotmail.com

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and

Sofia Lambropoulou

Department of Mathematics, National Technical University of Athens, Zografou campus, GR-15780 Athens, Greece

E-mail Address: sofia@math.ntua.gr

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https://doi.org/10.1142/S0218216519400078Cited by:7 (Source: Crossref)

This article is part of the issue:

Special Issue: Knots, Low-Dimensional Topology and Applications — Part I

Abstract

We prove that, in order to derive the HOMFLYPT skein module of the lens spaces $L (p, 1)$ from the HOMFLYPT skein module of the solid torus, $𝒮 (ST)$ , it suffices to solve an infinite system of equations obtained by imposing on the Lambropoulou invariant $X$ for knots and links in the solid torus, braid band moves that are performed only on the first moving strand of elements in a set $Λ^{aug}$ , augmenting the basis $Λ$ of $𝒮 (ST)$ .

Keywords:

AMSC: 57M27, 57M25, 57Q45, 20F36, 20C08

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