Endperiodic Maps via Pseudo-Anosov Flows

Explore the intricacies of endperiodic maps and their connection to pseudo-Anosov flows in this 51-minute lecture by Samuel Taylor at the Centre de recherches mathématiques (CRM). Delve into the fascinating world of infinite-type surface homeomorphisms and their isotopic relationships to first return maps of pseudo-Anosov suspension flows on fibered manifolds. Discover how these maps are conceptually derived by "spinning" fibers around surfaces in the boundary of the fibered cone. Examine the applications of spun pseudo-Anosov maps, including the definition and characterization of stretch factors for endperiodic maps, the relationship between Cantwell-Conlon foliation cones and Thurston's fibered cones, and the extension of log(stretch factor) to a convex entropy function on these cones. Gain insights into this collaborative research with Michael Landry and Yair Minsky, presented as part of the Workshop on Geometry of Subgroups held in May 2023.