Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds
Permanent link to this recordhttp://hdl.handle.net/20.500.12613/4580
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AbstractThis paper proves that every finite volume hyperbolic 3-manifold M contains a ubiquitous collection of closed, immersed, quasi-Fuchsian surfaces. These surfaces are ubiquitous in the sense that their preimages in the universal cover separate any pair of disjoint, non-asymptotic geodesic planes. The proof relies in a crucial way on the corresponding theorem of Kahn and Markovic for closed 3-manifolds. As a corollary of this result and a companion statement about surfaces with cusps, we recover Wise's theorem that the fundamental group of M acts freely and cocompactly on a CAT(0) cube complex.
Citation to related workMathematical Sciences Publishers
Has partGEOMETRY & TOPOLOGY
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