A Simple Geometric Representative for $\mu$ of a Point

TL;DR

This paper constructs a straightforward geometric representative for the  of a point in Donaldson theory on 4-manifolds, using reducible connections at a generic point.

Contribution

It introduces a simple geometric representative for  of a point in Donaldson theory, based on reducible connections at a generic point.

Findings

Provides a geometric representative with coefficient -1/4

Uses reducible connections at a generic point

Simplifies the understanding of  in Donaldson theory

Abstract

For $SU(2)$ (or $SO(3)$) Donaldson theory on a 4-manifold $X$, we construct a simple geometric representative for $\mu$ of a point. Let $p$ be a generic point in $X$. Then the set $\{ [A] | F_A^-(p) $ is reducible $\}$, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.