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Pré-Publication, Document De Travail Année : 2012

HOMFLY-PT skein module of singular links in the three-sphere

Résumé

For a ring $R$, we denote by $R[\mathcal L]$ the free $R$-module spanned by the isotopy classes of singular links in $\\mathbb S^3$. Given two invertible elements $x,t \in R$, the HOMFLY-PT skein module of singular links in $\mathbb S^3$ (relative to the triple $(R,t,x)$) is the quotient of $R[\mathcal L]$ by local relations, called skein relations, that involve $t$ and $x$. We compute the HOMFLY-PT skein module of singular links for any $R$ such that $(t^{-1}-t+x)$ and $(t^{-1}-t-x)$ are invertible. In particular, we deduce the Conway skein module of singular links.
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Dates et versions

hal-00707319 , version 1 (12-06-2012)

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Luis Paris, Emmanuel Wagner. HOMFLY-PT skein module of singular links in the three-sphere. 2012. ⟨hal-00707319⟩
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