EVENT DETAILS AND ABSTRACT

Title: The directed Fukaya category and Morse theory
Speaker: Joseph Johns
Speaker Info: Univesity of Chicago
Brief Description:
Special Note:
Abstract:

Let $f: N \longrightarrow \mathbb{R}$ be a Morse function and let $g$ be a Riemannian metric so that $(f,g)$ is Morse-Smale. Given this data I will explain how to construct an explicit model of a Lefschetz fibration $\pi = \pi_{(f,g)}: T^*N \longrightarrow \mathbb{C}$ which extends $f$ and has no further critical points. I will then relate the directed Fukaya category of $\pi$ to the flow category of $(N,f,g)$. If time permits, I will mention an application of these results to Arnold's nearby Lagrangian problem, building on work of Fukaya, Smith, and Seidel.