On Seifert fibered spaces bounding definite manifolds

TL;DR

This paper establishes inequalities that restrict embeddings of intersection lattices of Seifert fibered spaces into diagonal lattices, with applications to questions in 4-manifold topology and characterizations of bounding spaces.

Contribution

It introduces new inequalities for intersection lattices of Seifert fibered spaces and applies them to answer open questions and characterize bounding 4-manifolds.

Findings

Restrictions on embeddings of intersection lattices

Answer to Neumann-Zagier's question relating Donaldson's theorem and Fintushel-Stern's R-invariant

Characterization of Seifert fibered spaces bounding rational homology S^1 x D^3s

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.