Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

YouTube

Geometry and Topology of Hamiltonian Floer Complexes in Low-Dimension - Dustin Connery-Grigg

Institute for Advanced Study via YouTube

Overview

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.

Syllabus

Introduction
Motivation
Setting
Capped braids
Chain level PSS maps
First theorem
Mermbraised unlinked braids
Oriented singular foliations
Loops
Solar foliation
Reduction of chain complexity
La Calvez type foliations
Questions

Taught by

Institute for Advanced Study

Reviews

Start your review of Geometry and Topology of Hamiltonian Floer Complexes in Low-Dimension - Dustin Connery-Grigg

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.