On Seifert fibered spaces bounding definite manifolds

Ahmad Issa; Duncan McCoy

doi:10.2140/pjm.2020.304.463

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arXiv · 1807.10310

On Seifert fibered spaces bounding definite manifolds

Ahmad Issa·Duncan McCoy

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Abstract

We establish an inequality which gives strong restrictions on when the standard definite plumbing intersection lattice of a Seifert fibered space over $S^2$ can embed into a standard diagonal lattice, and give two applications. First, we answer a question of Neumann-Zagier on the relationship between Donaldson's theorem and Fintushel-Stern's $R$-invariant. We also give a short proof of the characterisation of Seifert fibered spaces which smoothly bound rational homology $S^1 \times D^3$'s.

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Ahmad Issa, Duncan McCoy. 2018-07-26. On Seifert fibered spaces bounding definite manifolds. https://doi.org/10.2140/pjm.2020.304.463

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