Totally Geodesic Seifert Surfaces in Hyperbolic Knot and Link Complements II

Colin Adams, Hanna Bennett, Christopher Davis, Michael Jennings, Jennifer Novak, Nicholas Perry, Eric Schoenfeld

Published 2004-11-16Version 1

We generalize the results of [AS], finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each the lift of a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots cannot possess totally geodesic Seifert surfaces by giving bounds on the width invariant in the presence of such a surface. Finally, we utilize these examples to demonstrate that the Six Theorem is sharp for knot complements in the 3-sphere.