The braid approach to the HOMFLYPT skein module of the lens spaces

Ioannis Diamantis, Sofia Lambropoulou*

*Corresponding author for this work

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In this paper we present recent results toward the computation of the HOMFLYPT skein module of the lens spaces L(p, 1), S (L(p, 1)), via braids. Our starting point is the knot theory of the solid torus ST and the Lambropoulou invariant, X, for knots and links in ST, the universal analogue of the HOMFLYPT polynomial in ST. The relation between S (L(p, 1)) and S(ST) is established in Diamantis et al. (J Knot Theory Ramif, 25: 13, 2016, [5]) and it is shown that in order to compute S (L(p, 1)), it suffices to solve an infinite system of equations obtained by performing all possible braid band moves on elements in the basis of S(ST),., presented in Diamantis and Lambropoulou (J Pure Appl Algebra, 220(2): 577-605, 2016, [4]). The solution of this infinite system of equations is very technical and is the subject of a sequel work (Diamantis and Lambropoulou, The HOMFLYPT skein module of the lens spaces L(p, 1) via braids, in preparation,
Original languageEnglish
Title of host publicationAlgebraic Modeling of Topological and Computational Structures and Applications
Subtitle of host publicationTHALES, Athens, Greece, July 1-3, 2015
EditorsSofia Lambropoulou, Doros Theodorou, Petros Stefaneas, Louis H. Kauffman
PublisherSpringer, Cham
ISBN (Electronic)978-3-319-68103-0
ISBN (Print)978-3-319-68102-3
Publication statusPublished - 2017
Externally publishedYes

Publication series

SeriesSpringer Proceedings in Mathematics and Statistics

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