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Abstract
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Given a noncompact quasi-Fuchsian surface in a finite volume hyperbolic 3–manifold,
we introduce a new invariant called the cusp thickness, that measures how far the
surface is from being totally geodesic. We relate this new invariant to the width of a
surface, which allows us to extend and generalize results known for totally geodesic
surfaces. We also show that checkerboard surfaces provide examples of such surfaces
in alternating knot complements and give examples of how the bounds apply to
particular classes of knots. We then utilize the results to generate closed immersed
essential surfaces.
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Keywords
hyperbolic 3–manifold, quasi-Fuchsian surface, totally
geodesic surface
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Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 20H10
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Publication
Received: 10 October 2006
Accepted: 24 January 2007
Published: 10 May 2007
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