On definite lattices bounded by a homology 3-sphere and Yang-Mills instanton Floer theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866929488492756992 |
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| author | Scaduto, Christopher |
| author_facet | Scaduto, Christopher |
| contents | Using instanton Floer theory, extending methods due to Froyshov, we determine the definite lattices that arise from smooth 4-manifolds bounded by certain homology 3-spheres. For example, we show that for +1 surgery on the (2,5) torus knot, the only non-diagonal lattices that can occur are E8 and the indecomposable unimodular definite lattice of rank 12, up to diagonal summands. We require that our 4-manifolds have no 2-torsion in their homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_07875 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On definite lattices bounded by a homology 3-sphere and Yang-Mills instanton Floer theory Scaduto, Christopher Geometric Topology 57R57, 57M99 Using instanton Floer theory, extending methods due to Froyshov, we determine the definite lattices that arise from smooth 4-manifolds bounded by certain homology 3-spheres. For example, we show that for +1 surgery on the (2,5) torus knot, the only non-diagonal lattices that can occur are E8 and the indecomposable unimodular definite lattice of rank 12, up to diagonal summands. We require that our 4-manifolds have no 2-torsion in their homology. |
| title | On definite lattices bounded by a homology 3-sphere and Yang-Mills instanton Floer theory |
| topic | Geometric Topology 57R57, 57M99 |
| url | https://arxiv.org/abs/1805.07875 |