TL;DR
This paper surveys gauge theory for families and explores its applications in comparing the diffeomorphism and homeomorphism groups of 4-manifolds up to 2021.
Contribution
It provides a comprehensive overview of gauge theory for families and its role in understanding 4-manifold topology.
Findings
Comparison between diffeomorphism and homeomorphism groups of 4-manifolds.
Applications of gauge theory for families in topology.
Summary of developments up to 2021.
Abstract
This article surveys gauge theory for families and its applications to the comparison between the diffeomorphism group and the homeomorphism group of -manifolds, up to 2021.
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