Totally geodesic boundaries of knot complements

Kent, Richard, IV

doi:10.1090/S0002-9939-05-07969-4

Totally geodesic boundaries of knot complements
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by Richard P. Kent IV PDF

Proc. Amer. Math. Soc. 133 (2005), 3735-3744 Request permission

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.

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