FSU-UF Topology Meeting

Title: Pseudo-Anosov flows in graph manifolds with periodic pieces

Speaker: Russ Waller (Florida State University)

Abstract: In their recent work, T. Barbot and S. Fenley demonstrate that the structure of pseudo-Anosov flows on Seifert pieces of totally periodic graph manifolds (graph manifolds where all pieces of the torus decomposition are periodic) is actually quite rigid, and can be fully described using what are called fat graphs. We study these fat graphs and the graphs they retract onto, called flow graphs. In particular, we determine precisely which surfaces are fat graphs. Also, we characterize the surfaces that are fat graphs with the extra restrictions on flow graphs needed to guarantee that the corresponding flows on the 3-manifold are pseudo-Anosov. We further determine the required valence of each vertex in order to understand which prongs the resulting pseudo-Anosov flow may have, and how many.