Superconformal simple type and Witten's conjecture

TL;DR

This paper proves that for certain four-manifolds with specific topological properties, the SO(3)-monopole cobordism formula confirms Witten's conjecture linking Donaldson and Seiberg-Witten invariants, assuming Seiberg-Witten simple type.

Contribution

It establishes a connection between the SO(3)-monopole cobordism formula and Witten's conjecture for four-manifolds with specific conditions, under the assumption of Seiberg-Witten simple type.

Findings

Witten's conjecture holds for four-manifolds with $b^1=0$, $b^+ ext{ odd} ext{ and } ext{at least }3$

The SO(3)-monopole cobordism formula implies Witten's conjecture in this setting

Seiberg-Witten simple type condition is crucial for the result

Abstract

Let $X$ be a smooth, closed, connected, orientable four-manifold with $b^1(X)=0$ and $b^+(X)\geq 3$ and odd. We show that if $X$ has Seiberg-Witten simple type, then the SO(3)-monopole cobordism formula of Feehan and Leness (2002) implies Witten's Conjecture relating the Donaldson and Seiberg-Witten invariants.