A survey on skein modules via braids

2023/11/11 by Diamantis, Ioannis · 2 citations
#20C08 #20F36 #20F38 #57K10 #57K12 #57K14 #57K31 #57K35 #57K45 #57K99 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2311.06556

Abstract

In this paper we present recent results on the computation of skein modules of 3-manifolds using braids and appropriate knot algebras. Skein modules generalize knot polynomials in S³ to knot polynomials in arbitrary 3-manifolds and they have become extremely essential algebraic tools in the study of 3-manifolds. In this paper we present the braid approach to the HOMFLYPT and the Kauffman bracket skein modules of the Solid Torus ST and the lens spaces L(p,1) and S¹× S².

Cited by

• From annular to toroidal knotoids and their universal bracket polynomials
• The HOMFLYPT skein module of S¹ × S² via braids

Related

• 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)
• An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids
• 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)