Volume 7, issue 2 (2007)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Noncompact Fuchsian and quasi-Fuchsian surfaces in hyperbolic 3–manifolds

Colin Adams

Algebraic & Geometric Topology 7 (2007) 565–582
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.

Keywords
hyperbolic 3–manifold, quasi-Fuchsian surface, totally geodesic surface
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 20H10
References
Publication
Received: 10 October 2006
Accepted: 24 January 2007
Published: 10 May 2007
Authors
Colin Adams
Department of Mathematics and Statistics
Williams College
Williamstown, MA 01267