Kauffman bracket skein module of two families of Seifert manifolds

2024/09/14 by Minyi Liang, Liang, Minyi, Xiao Wang +2
Mathematics · #57K10 #57K31 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2409.09438

openalex publication_date 2024/09/14 · openalex created_date 2024/10/27 · openalex updated_date 2026/07/28

Abstract

We compute the Kauffman bracket skein modules of Seifert manifolds Σ_0,1((k₁,1),(k₂,1)) and Σ_0,0((k₁,1),(k₂,1),(k₃,1)) by providing presentations of them. From the obtained presentations, we show that the Kauffman bracket skein modules of Σ_0,1((k₁,1),(k₂,1)) are free with infinitely many generators when k₁,k₂≥ 1 and that of Σ_0,0((k₁,1),(k₂,1),(k₃,1)) are finitely generated when k₁,k₂,k₃ ≥ 2. We also show that the empty link in either case is not trivial.

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