Geometry & Topology Seminar: "Anosov flows in higher dimensions"

Abstract: The topological study of Anosov flows on 3-manifolds have garnered a fair amount of attention in the past decades. Research showed both interesting connections between the dynamics and the topology of the manifold, and also found a huge diversity, obtained by surgery techniques, of Anosov flows in 3-manifolds. When one consider Anosov flows in higher dimensions, however, almost nothing is known. In particular, there is a dire need of examples. In 1979, Franks and Williams suggested a way of building non-transitive Anosov flows in higher dimensional dimensions, and nothing else came up since then.
In this talk, I will explain a partial classification result about (fiberwise) Anosov flows that implies that Franks and Williams suggestion does not create Anosov flows in higher dimension. If time permits, I will also explain how to modify Franks and Williams 3-dimensional example to obtain higher dimensional examples. (Joint work with C. Bonatti, A. Gogolev and F. Rodriguez Hertz).

Host: Steven Frankel