Minimality of the Compact-Open Topology on Diffeomorphism and Homeomorphism Groups

Explore a mathematical lecture on the minimality of compact-open topology in diffeomorphism groups. Delve into recent research proving that the compact-open topology restricted to the diffeomorphism group of a manifold without boundary, in dimensions other than 3, is a minimal element in the lattice of Hausdorff group topologies. Learn how this result extends to homeomorphism groups for dimensions other than 3 and 4, and discover its implications for K. Mann's automatic continuity results, leading to the conclusion that homeomorphism groups admit a unique separable Hausdorff group topology. This 44-minute talk, presented by Javier de la Nuez González at the Erwin Schrödinger International Institute for Mathematics and Physics, was part of the Workshop on "Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics."