Knots having the same Seifert form and primary decomposition of knot concordance

2017/08/20 by Taehee Kim, Kim, Taehee
Mathematics · #57M25 #57N70 #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.1708.05962

openalex publication_date 2017/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We show that for each Seifert form of an algebraically slice knot with nontrivial Alexander polynomial, there exists an infinite family of knots having the Seifert form such that the knots are linearly independent in the knot concordance group and not concordant to any knot with coprime Alexander polynomial. Key ingredients for the proof are Cheeger-Gromov-von Neumann rho-invariants for amenable groups developed by Cha and Orr and polynomial splittings of metabelian rho-invariants.

Citations

• 2-torsion in the grope and solvable filtrations of knots
• Knot concordance, Whitney towers and L 2 -signatures
• Polynomial splittings of correction terms and doubly slice knots
• A Topological Approach to Cheeger‐Gromov Universal Bounds for von Neumann ρ‐Invariants

Related

• Infinite family of non-concordant knots having the same Seifert form
• Primary decomposition of knot concordance and von Neumann rho-invariants
• Polynomial splittings of metabelian von Neumann rho-invariants
• Equivariant algebraic concordance of strongly invertible knots
• One-bipolar topologically slice knots and primary decomposition