Abundant quasifuchsian surfaces in cusped hyperbolic 3-manifolds

Abundant quasifuchsian surfaces in cusped hyperbolic 3-manifolds

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Dave Futer , Temple University/IAS
Fine Hall 314

I will discuss a proof that every finite volume hyperbolic 3-manifold M contains an abundant collection of immersed, $\pi_1$-injective surfaces. These surfaces are abundant in the sense that their lifts to the universal cover separate any pair of disjoint geodesic planes. The proof relies in a major way on the corresponding theorem of Kahn and Markovic for closed 3-manifolds. As a corollary, we recover Wise's theorem that the fundamental group of M is acts properly and cocompactly on a cube complex. This is joint work with Daryl Cooper.