Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
The Verjosky conjecture states that every codimension one Anosov flow in dimensions 4 or higher is orbitally equivalent to a suspension Anosov flow. Codimension one means that either the weak stable or weak unstable foliation is codimension one. This conjecture is 50 years old. In joint work with K. Mann and R. Potrie we construct
infinitely many counterexamples to the conjecture in 4-manifolds. To achieve that we need a closed hyperbolic 3-manifold M, a faithful minimal representation of \pi_1(M) into Homeo^+(S^1) (the circle), and a group equivariant Cannon-Thurston map from S^1 to the sphere at infinity of hyperbolic 3-space. This allows to construct a topological Anosov flow in dimension 4, and we are able to construct a C^1 model from this flow.