Explore a 31-minute lecture on the geometry and topology of Hamiltonian Floer complexes in low-dimension, presented by Dustin Connery-Grigg from Université de Montreal. Delve into two key results relating non-degenerate Hamiltonian isotopies on surfaces to their Floer complex structures. Examine a topological characterization of Floer chains representing the fundamental class in CF∗(H,J) and lying in the image of chain-level PSS maps, leading to a novel symplectically bi-invariant norm on Hamiltonian diffeomorphisms. Investigate the geometric interpretation of portions of the Hamiltonian Floer chain complex in terms of positively transverse singular foliations of the mapping torus. Discover how this construction provides a Floer-theoretic approach to 'torsion-low' foliations in Le Calvez's theory, bridging symplectic geometry and surface homeomorphisms. Follow the lecture's progression through topics such as capped braids, membraised unlinked braids, oriented singular foliations, and solar foliations, culminating in a discussion on the reduction of chain complexity and Le Calvez type foliations. Read more