On the mu-bar invariant of rational surface singularities

TL;DR

This paper demonstrates that for rational surface singularities with odd determinant, the mu-bar invariant acts as an obstruction to the link bounding a rational homology 4-ball, linking algebraic invariants with topological properties.

Contribution

It identifies the mu-bar invariant with a Heegaard Floer correction term and establishes its role as an obstruction in the topology of rational surface singularities.

Findings

mu-bar invariant obstructs bounding rational homology 4-balls

mu-bar is identified with Heegaard Floer correction term

applicable to rational surface singularities with odd determinant

Abstract

We show that for rational surface singularities with odd determinant the mu-bar invariant defined by W. Neumann is an obstruction for the link of the singularity to bound a rational homology 4-ball. We identify the mu-bar invariant with the corresponding correction term in Heegaard Floer theory.