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This paper computes the homflypt skein module in S1 x S2, extending the Lambropoulou invariant's applicability.
In this paper we compute the HOMFLYPT skein module of S¹ × S²\, \, L(0, 1), denoted S(S¹ × S²), using braid-theoretic techniques. We extend the Lambropoulou invariant, X, for links in the solid torus ST to links in S¹ × S², by solving an infinite system of equations of the form X_a = X_bbm(a), where $bbm(a)$ denotes all possible band moves applied to a, for all a in a basis of S(ST). We show that the free part of S(S¹ × S²) is generated by the empty link, while all other elements are torsion.
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Ioannis Diamantis (2025) studied this question.
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