Noncompact Fuchsian and quasi-Fuchsian surfaces in hyperbolic 3–manifolds

Adams, Colin

doi:10.2140/agt.2007.7.565

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Noncompact Fuchsian and quasi-Fuchsian surfaces in hyperbolic 3–manifolds

Colin Adams

Algebraic & Geometric Topology 7 (2007) 565–582

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.

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

Volume 7, issue 2 (2007)