Instanton Floer Homology and Heegaard Diagrams

Explore the intersection of instanton Floer homology and Heegaard diagrams in this conference talk delivered by Zhenkun Li from Stanford University. Delve into the powerful invariants for three-manifolds and knots introduced by Floer in the 1980s, and discover how they have led to significant breakthroughs, including the approval of the Property P conjecture. Learn about the combinatorial methods of Heegaard diagrams for describing 3-manifolds and understand the previously unexplored explicit relations between these two mathematical objects. Gain insights into extracting information about the instanton Floer homology of a 3-manifold Y from its Heegaard diagrams, and explore potential applications and future directions of this research. This talk, based on joint work with Baldwin and Ye, offers a deep dive into cutting-edge developments in gauge theory and low-dimensional topology.