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Junior Topology
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Teddy Weisman, Zoom: Kleinian groups and structural stability from dynamics
Wednesday, September 16, 2020, 02:00pm - 03:00pm
When M is a hyperbolic 3-manifold, there is a homomorphism from the fundamental group of M to the group PSL(2, C) which determines the hyperbolic structure up to isometry. Under certain conditions, this homomorphism is injective and structurally stable: small deformations of the image inside of PSL(2,C) can yield different isomorphic copies of pi_1(M) in PSL(2,C) and (possibly) different hyperbolic structures on M. The plan for this talk is to give an introduction to hyperbolic 3-space and hyperbolic 3-manifolds, and then sketch a proof of this stability result. We'll follow a classical approach due to Sullivan, which characterizes convex cocompact hyperbolic 3-manifolds using a dynamical (expansion) condition on the boundary of hyperbolic space.
Location: Zoom

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