Totally Geodesic Seifert Surfaces in Hyperbolic Knot and Link Complements II

Details Totally Geodesic Seifert Surfaces in Hyperbolic Knot and Link Complements II Totally Geodesic Seifert Surfaces in Hyperbolic Knot and Link Complements II

2004-11-16

arxiv.org/abs/math/0411358v1

Mathematics

Geometric Topology

Scientific paper

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.

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