Totally geodesic boundaries of knot complements
Geometric Topology
2007-05-23 v2
Abstract
Given a compact orientable 3-manifold M whose boundary is a hyperbolic surface and a simple closed curve C in its boundary, every knot in M is homotopic to one whose complement admits a complete hyperbolic structure with totally geodesic boundary in which the geodesic representative of C is as small as you like.
Cite
@article{arxiv.math/0403445,
title = {Totally geodesic boundaries of knot complements},
author = {Richard P. Kent},
journal= {arXiv preprint arXiv:math/0403445},
year = {2007}
}
Comments
10 pages, no figures, the exposition has been polished, typographical errors corrected, a modicum of detail added, to appear in Proceedings of the AMS