2024/05/07 by Rhea Palak Bakshi, Bakshi, Rhea Palak, Seongjeong Kim +3
Mathematics · #57K10 #57K31 #Algebraic and Geometric Analysis #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Analysis and Transform Methods #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2405.04337
openalex publication_date 2024/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Determining the structure of the Kauffman bracket skein module of all 3-manifolds over the ring of Laurent polynomials \mathbb Z[A± 1] is a big open problem in skein theory. Very little is known about the skein module of non-prime manifolds over this ring. In this paper, we compute the Kauffman bracket skein module of the 3-manifold (S1 × S2) # (S1 × S2) over the ring \mathbb Z[A± 1]. We do this by analysing the submodule of handle sliding relations, for which we provide a suitable basis. Along the way we compute the Kauffman bracket skein module of (S1 × S2) # (S1 × D2). We also show that the skein module of (S1 × S2) # (S1 × S2) does not split into the sum of free and torsion submodules. Furthermore, we illustrate two families of torsion elements in this skein module.