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

Ioannis Diamantis; Sofia Lambropoulou

doi:10.1142/S0218216519400078

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

Research output: Contribution to journal › Article › Academic › peer-review

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 language	English
Article number	1940007
Number of pages	25
Journal	Journal of Knot Theory and Its Ramifications
Volume	28
Issue number	11
DOIs	https://doi.org/10.1142/S0218216519400078
Publication status	Published - Oct 2019
Externally published	Yes

Keywords

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

Access to Document

10.1142/S0218216519400078

Cite this

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

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).",

keywords = "HOMFLYPT skein module, solid torus, Iwahori-Hecke algebra of type B, mixed links, mixed braids, lens spaces",

author = "Ioannis Diamantis and Sofia Lambropoulou",

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N2 - 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).

AB - 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).

KW - HOMFLYPT skein module

KW - solid torus

KW - Iwahori-Hecke algebra of type B

KW - mixed links

KW - mixed braids

KW - lens spaces

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DO - 10.1142/S0218216519400078

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JO - Journal of Knot Theory and Its Ramifications

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