Definite fillings of lens spaces

Paolo Aceto; Duncan McCoy; JungHwan Park

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arXiv · 2208.02586

Definite fillings of lens spaces

Paolo Aceto·Duncan McCoy·JungHwan Park

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Abstract

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.

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Paolo Aceto, Duncan McCoy, JungHwan Park. 2022-08-04. Definite fillings of lens spaces. https://arxiv.org/abs/2208.02586

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