Tamed to compatible when b^(2+) = 1 and b^1 = 2

TL;DR

This paper addresses a gap in a previous proof related to symplectic 4-manifolds with specific Betti numbers, providing clarification and correction to ensure the theorem's validity.

Contribution

It identifies and fills a gap in the proof of a key theorem concerning symplectic forms on 4-manifolds with particular Betti number conditions.

Findings

The proof gap in the original theorem is successfully filled.

The corrected proof confirms the theorem's validity for the specified case.

Clarifies conditions under which the main theorem applies.

Abstract

Weiyi Zhang noticed recently a gap in the proof of the main theorem of the authors article "Tamed to compatible: Symplectic forms via moduli space integration" [T] for the case when the symplectic 4-manifold in question has first Betti number 2 (and necessarily self-dual second Betti number 1). This note explains how to fill this gap.