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2007 Noncompact Fuchsian and quasi-Fuchsian surfaces in hyperbolic 3–manifolds
Colin Adams
Algebr. Geom. Topol. 7(2): 565-582 (2007). DOI: 10.2140/agt.2007.7.565

Abstract

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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Colin Adams. "Noncompact Fuchsian and quasi-Fuchsian surfaces in hyperbolic 3–manifolds." Algebr. Geom. Topol. 7 (2) 565 - 582, 2007. https://doi.org/10.2140/agt.2007.7.565

Information

Received: 10 October 2006; Accepted: 24 January 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1143.57008
MathSciNet: MR2308957
Digital Object Identifier: 10.2140/agt.2007.7.565

Subjects:
Primary: 57M50
Secondary: 20H10

Rights: Copyright © 2007 Mathematical Sciences Publishers

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