English

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.

Keywords

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

R2 v1 2026-07-22T17:03:45.318Z