Algebraic Structure of Area-Preserving Homeomorphism Groups - Lecture 4

Explore the fourth lecture in a series on the algebraic structure of groups of area-preserving homeomorphisms, delivered by Sobhan Seyfaddini from Sorbonne Université as part of the Simons Semester on Dynamics. Delve into recent developments addressing Albert Fathi's influential question from the 1970s regarding the simplicity of compactly supported area-preserving homeomorphisms on compact surfaces. Examine the construction and application of link spectral invariants, crucial numerical tools used to solve Fathi's more general inquiry. Gain insights into Lagrangian Floer homology and its associated spectral invariants, which form the foundation for these groundbreaking results. Discover how these concepts contribute to understanding the non-simplicity of certain groups of area-preserving homeomorphisms, particularly on the 2-disc, and their implications for other compact surfaces.