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

Ioannis Diamantis*, Sofia Lambropoulou

*Corresponding author for this work

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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, 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 Lambda(aug), augmenting the basis. of S(ST).

Original languageEnglish
Article number1940007
Number of pages25
JournalJournal of Knot Theory and Its Ramifications
Volume28
Issue number11
DOIs
Publication statusPublished - Oct 2019
Externally publishedYes

Keywords

  • HOMFLYPT skein module
  • solid torus
  • Iwahori-Hecke algebra of type B
  • mixed links
  • mixed braids
  • lens spaces

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