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

We establish an inequality which gives strong restrictions on when the standard definite plumbing intersection lattice of a Seifert fibered space over S2 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 S1 × D3’s.

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Seifert fibered spaces, Donaldson's theorem, lattices, definite 4-manifolds
Mathematical Subject Classification 2010
Primary: 57M27
Received: 29 August 2018
Revised: 20 August 2019
Accepted: 20 August 2019
Published: 12 February 2020
Ahmad Issa
Department of Mathematics
University of British Columbia
Vancouver, BC
Duncan McCoy
Départment de Mathématiques
Université du Québec à Montréal
Montréal, QC