Dynamical Resistance Day
Title: Inequivalent Anosov flows on hyperbolic 3-manifolds (video)
In the 1980s, Goodman showed that there were many hyperbolic 3-manifolds which admit Anosov flows. Since then it has been an open question (attributed to Christy in Kirby's problem list) whether there exist hyperbolic manifolds which admit arbitrarily many distinct Anosov flows. Known constructions (e.g. of Beguin-Bonatti-Yu) for producing many flows on the same manifold typically use tools that don't apply to hyperbolic manifolds.
I will explain recent joint work with Jonathan Bowden that gives a positive answer to Christy's question. The talk will describe the construction of the Anosov flows, and some sketch of the proof that these are not orbit equivalent.