Diffeomorphism groups and gauge theory for families

TL;DR

This paper surveys gauge theory for families, emphasizing its recent applications to diffeomorphism groups of 4-manifolds developed between 2021 and 2025.

Contribution

It compiles recent developments in gauge theory applications to diffeomorphism groups of 4-manifolds from 2021 to 2025.

Findings

New insights into diffeomorphism groups of 4-manifolds

Applications of gauge theory to family classifications

Recent progress in 4-manifold topology

Abstract

This article provides a survey of gauge theory for families, with a particular focus on its applications to diffeomorphism groups of $4$-manifolds that were developed during the period 2021--2025.