The HOMFLYPT skein module of S¹ × S² via braids

2025/07/17 by Diamantis, Ioannis
#20C08 #20F36 #57K10 #57K14 #57K31 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2507.12826

Abstract

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_\widehata = X_\widehatbbm(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.

Citations

• A survey on skein modules via braids
• The Kauffman bracket skein module of the complement of (2, 2p+1)-torus knots via braids
• HOMFLYPT skein sub-modules of the lens spaces L(p, 1)
• An important step for the computation of the HOMFLYPT skein module of the lens spaces L(p,1) via braids
• An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids
• Topological steps toward the Homflypt skein module of the lens spaces\n L(p,1) via braids
• The braid approach to the HOMFLYPT skein module of the lens spaces L(p,1)
• Braid equivalence in 3-manifolds with rational surgery description
• Algebraic Markov equivalence for links in 3-manifolds
• Knot theory related to generalized and cyclotomic Hecke algebras of type B
• Markov's theorem in 3--manifolds

Related

• An important step for the computation of the HOMFLYPT skein module of the lens spaces L(p,1) via braids
• HOMFLYPT skein sub-modules of the lens spaces L(p, 1)
• The Kauffman bracket skein module of S¹× S² via braids
• The braid approach to the HOMFLYPT skein module of the lens spaces L(p,1)
• Topological steps toward the Homflypt skein module of the lens spaces\n L(p,1) via braids