TY - GEN

T1 - The braid approach to the HOMFLYPT skein module of the lens spaces

AU - Diamantis, Ioannis

AU - Lambropoulou, Sofia

PY - 2017

Y1 - 2017

N2 - 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,

AB - 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,

U2 - 10.1007/978-3-319-68103-0_7

DO - 10.1007/978-3-319-68103-0_7

M3 - Conference article in proceeding

SN - 978-3-319-68102-3

T3 - Springer Proceedings in Mathematics and Statistics

SP - 143

EP - 176

BT - Algebraic Modeling of Topological and Computational Structures and Applications

A2 - Lambropoulou, Sofia

A2 - Theodorou, Doros

A2 - Stefaneas, Petros

A2 - Kauffman, Louis H.

PB - Springer, Cham

ER -