On Seifert fibered spaces bounding definite manifolds

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 $S^{1} \times D^{3}$ ’s.

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Keywords

Seifert fibered spaces, Donaldson's theorem, lattices, definite 4-manifolds

Mathematical Subject Classification 2010

Primary: 57M27

Milestones

Received: 29 August 2018

Revised: 20 August 2019

Accepted: 20 August 2019

Published: 12 February 2020

Authors

Ahmad Issa
Department of Mathematics University of British Columbia Vancouver, BC Canada

Duncan McCoy
Départment de Mathématiques Université du Québec à Montréal Montréal, QC Canada

Vol. 304, No. 2, 2020

Ahmad Issa and Duncan McCoy

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors