Almost complex 4-manifolds with vanishing first Chern class

TL;DR

This paper explores the constraints on the topology of certain 4-manifolds with almost complex structures and zero first Chern class, using Seiberg-Witten invariants to establish bounds on their signature.

Contribution

It establishes new bounds on the signature of almost complex 4-manifolds with vanishing first Chern class based on Seiberg-Witten invariants, especially for symplectic manifolds of Kodaira dimension zero.

Findings

Bounds on the signature of such 4-manifolds derived from Seiberg-Witten invariants.

Application of results to symplectic 4-manifolds with Kodaira dimension zero.

Insights into the topology of almost complex 4-manifolds with specific invariants.

Abstract

An odd Seiberg-Witten invariant imposes bounds on the signature of a closed, almost complex 4-manifold with vanishing first Chern class. This applies in particular to symplectic 4-manifolds of Kodaira dimension zero.