A triple torsion linking form and 3-manifolds in $S^4$
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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916912955392000 |
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| author | Freedman, Michael Krushkal, Vyacheslav |
| author_facet | Freedman, Michael Krushkal, Vyacheslav |
| contents | Given a rational homology 3-sphere $M$, we introduce a triple linking form on $H_1(M; \mathbb{Z})$, 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 $S^4$, extending a 1938 theorem of Hantzsche. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_11941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A triple torsion linking form and 3-manifolds in $S^4$ Freedman, Michael Krushkal, Vyacheslav Geometric Topology Given a rational homology 3-sphere $M$, we introduce a triple linking form on $H_1(M; \mathbb{Z})$, 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 $S^4$, extending a 1938 theorem of Hantzsche. |
| title | A triple torsion linking form and 3-manifolds in $S^4$ |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2506.11941 |