# A connection between pseudo-Anosov flows and sutured Floer homology

# A connection between pseudo-Anosov flows and sutured Floer homology

A pseudo-Anosov flow is a flow on a 3-manifold with a special kind of dynamics. There are known connections between pseudo-Anosov flows and foliations --- certain taut foliations are known to admit transverse pseudo-Anosov flows, and there are known connections between pseudo-Anosov flows and orderings --- pseudo-Anosov flows induce circular orders, which can sometimes be lifted to left orders. In contrast, there are few known connections between pseudo-Anosov flows and the remaining area in the L-space conjecture: Heegaard Floer homology. In this talk, we present a construction in joint work with Antonio Alfieri, which allows one to compute from the dynamical data of a pseudo-Anosov flow the sutured Floer homology of a naturally associated sutured manifold. We will also explain some future directions that we hope this construction will find applications in.