Low Dimensional Topology and Circle-valued Morse Functions

Explore the intricacies of Khovanov homology for infinite torus braids in this conference talk by Christine Lee from Texas State University. Delve into the characterization of a simplified complex derived from the Khovanov complex of torus braids on n strands. Learn about recent collaborative work that provides insights into this central object in quantum topology. Discover the application of this research, including a formula for the Khovanov homology of torus braids on 3-strands and its implications for Plamenevskaya's invariant. The talk covers various aspects such as introduction to homology, coefficient vectors, surgery theorems, stable homology, Jones Wenzel projector, differentials, and structure theorems. Gain a deeper understanding of the challenges in determining the differentials of conjectured forms of the complex and the progress made towards related conjectures by Gorsky-Oblomkov-Rasmussen-Shende.