Triple linking and rational homology cobordism

2025/11/05 by Ryan Stees, Stees, Ryan
Mathematics · Computer Science · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2511.03818

Abstract

If a rational homology 3-sphere M bounds a rational homology 4-ball W, then the kernel of the inclusion-induced homomorphism H₁(M;ℤ)→ H₁(W;ℤ) is a Lagrangian for the ℚ/ℤ-valued torsion linking form λ₂ on H₁(M;ℤ). In this short paper, we prove that the Freedman-Krushkal triple torsion linking form λ₃ (arXiv:2506.11941v3) vanishes on this Lagrangian under the assumption that H₂(W;ℤ)=0. We then pose several questions about topological rational homology cobordism.

Citations

• A triple torsion linking form and 3-manifolds in S⁴
• Algebraic classification of linking pairings on 3-manifolds
• Einlagerung von Mannigfaltigkeiten in euklidische R�ume

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