#### Vol. 304, No. 2, 2020

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On Seifert fibered spaces bounding definite manifolds

### Ahmad Issa and Duncan McCoy

Vol. 304 (2020), No. 2, 463–480
##### 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 and Zagier on the relationship between Donaldson’s theorem and Fintushel–Stern’s $R$-invariant. We also give a short proof of the characterization of Seifert fibered spaces which smoothly bound rational homology ${S}^{1}×{D}^{3}$’s.

##### Keywords
Seifert fibered spaces, Donaldson's theorem, lattices, definite 4-manifolds
Primary: 57M27