Abstract
We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering 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.
| Original language | English |
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| Journal | Journal of Differential Geometry |
| Volume | 79 |
| Issue number | 1 |
| Pages (from-to) | 1-23 |
| ISSN | 0022-040X |
| Publication status | Published - 2008 |