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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00707319
Contributor : Luis Paris <>
Submitted on : Tuesday, June 12, 2012 - 2:21:58 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Thursday, December 15, 2016 - 1:47:33 PM

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  • HAL Id : hal-00707319, version 1
  • ARXIV : 1206.2521

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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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