Given an Anosov flow in a closed 3-manifold, it is possible to construct many other ones by doing Fried surgeries along periodic orbits. The graph whose vertices are the pairs (Anosov flow,3-manifold) and two vertices are connected with an edge if there is a Fried surgery transforming one into the other, is called the Graph of Anosov Flows. Up to the reasonable hypothesis, one open question is the connectivity of this graph. Our aim in this talk is to see how this question can be translated into a problem of Affine Structures on Closed Surfaces and, even more, Affine Interval Exchange Transformations.

Zoom link: https://rochester.zoom.us/j/94706402472