Totally Geodesic Seifert Surfaces in Hyperbolic Knot and Link Complements II
Geometric Topology
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0411358,
title = {Totally Geodesic Seifert Surfaces in Hyperbolic Knot and Link Complements II},
author = {Colin Adams and Hanna Bennett and Christopher Davis and Michael Jennings and Jennifer Novak and Nicholas Perry and Eric Schoenfeld},
journal= {arXiv preprint arXiv:math/0411358},
year = {2007}
}