Characteristic classes via 4-dimensional gauge theory

TL;DR

This paper introduces a novel method for constructing characteristic classes of 4-manifold bundles by utilizing $SO(3)$-Yang-Mills and Seiberg-Witten theories in a family setting.

Contribution

It develops a new framework connecting gauge theories with characteristic classes for 4-manifold bundles, expanding the tools available in differential topology.

Findings

Constructed characteristic classes using gauge theory techniques.

Established relationships between gauge theory invariants and bundle topology.

Provided new invariants for 4-manifold bundles.

Abstract

We construct characteristic classes of 4-manifold bundles using $SO(3)$-Yang-Mills theory and Seiberg-Witten theory for families.