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

Ioannis Diamantis; Sofia Lambropoulou

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arXiv · 1802.09376

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

Ioannis Diamantis·Sofia Lambropoulou

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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, $\mathcal{S}({\rm ST})$, 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 $\Lambda^{aug}$, augmenting the basis $\Lambda$ of $\mathcal{S}({\rm ST})$.

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Ioannis Diamantis, Sofia Lambropoulou. 2018-02-23. An important step for the computation of the HOMFLYPT skein module of the lens spaces $L(p,1)$ via braids. https://arxiv.org/abs/1802.09376

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