Richard P. Kent IV
Published 2004-03-25, updated 2004-07-21Version 2
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.
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
Angle structures and hyperbolic $3$-manifolds with totally geodesic boundary
Proving a manifold to be hyperbolic once it has been approximated to be so
Distinguished waves and slopes in genus two
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