Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond - Lecture 4

Explore the intricacies of countable subgroups within homeomorphism groups in this advanced mathematics lecture. Delve into the examination of finitely generated and countable subgroups with specific properties, focusing on regularity in one-dimensional cases. Gain insights into critical regularity through the speaker's collaborative work with S. Kim. Follow the outline of a program aimed at extending one-dimensional results to higher dimensions. Discover recent findings on the model theory of homeomorphism groups for compact manifolds, presented in collaboration with S. Kim and J. de la Nuez Gonzalez. Contemplate potential future generalizations of these concepts in the field of mathematical topology and group theory.