Diffeomorphism groups and gauge theory for families

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.

arXiv comment27 pages. To appear in Sugaku Expositions. This article is an English translation of a Japanese survey article. It is also a slightly expanded version of the proceedings article for the 2025 Georgia International Topology Conference entitled "Diffeomorphism groups of 4-manifolds and gauge theory for families."