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    Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds

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    1705.02890v3.pdf
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    Genre
    Pre-print
    Date
    2019
    Author
    Cooper, Daryl
    Futer, David
    Subject
    math.GT
    math.GT
    math.GR
    57M50, 30F40, 20H10, 20F65
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/4580
    
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    DOI
    10.2140/gt.2019.23.241
    Abstract
    This 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 work
    Mathematical Sciences Publishers
    Has part
    GEOMETRY & TOPOLOGY
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/4562
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