A triple torsion linking form and 3-manifolds in S⁴

2025/06/13 by Michael Freedman, Freedman, Michael, Vyacheslav Krushkal +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2506.11941

openalex publication_date 2025/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a rational homology 3-sphere M, we introduce a triple linking form on H₁(M; ℤ), defined when the classical torsion linking pairing of three homology classes vanishes pairwise. If M is the boundary of a simply-connected 4-manifold N, the triple linking form can be computed in terms of the higher order intersection form on N, introduced by Matsumoto. We use these methods to formulate an embedding obstruction for rational homology spheres in S⁴, extending a 1938 theorem of Hantzsche.

Citations

• Enhanced Hantzsche Theorem
• Einlagerung von Mannigfaltigkeiten in euklidische R�ume

Cited by

• Triple linking and rational homology cobordism

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