Definite fillings of lens spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909352099577856 |
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| author | Aceto, Paolo McCoy, Duncan Park, JungHwan |
| author_facet | Aceto, Paolo McCoy, Duncan Park, JungHwan |
| contents | This paper considers the problem of determining the smallest (as measured by the second Betti number) smooth negative-definite filling of a lens space. The main result is to classify those lens spaces for which the associated negative-definite canonical plumbing is minimal. The classification takes the form of a list of 10 "forbidden" subgraphs that cannot appear in the plumbing graph if the corresponding plumbed 4-manifold is minimal. We also show that whenever the plumbing is minimal any other negative-definite filling for the given lens space has the same intersection form up to addition of diagonal summands. Consequences regarding smooth embeddings of lens spaces in 4-manifolds are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_02586 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Definite fillings of lens spaces Aceto, Paolo McCoy, Duncan Park, JungHwan Geometric Topology This paper considers the problem of determining the smallest (as measured by the second Betti number) smooth negative-definite filling of a lens space. The main result is to classify those lens spaces for which the associated negative-definite canonical plumbing is minimal. The classification takes the form of a list of 10 "forbidden" subgraphs that cannot appear in the plumbing graph if the corresponding plumbed 4-manifold is minimal. We also show that whenever the plumbing is minimal any other negative-definite filling for the given lens space has the same intersection form up to addition of diagonal summands. Consequences regarding smooth embeddings of lens spaces in 4-manifolds are also discussed. |
| title | Definite fillings of lens spaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2208.02586 |