Totally geodesic boundaries of knot complements

Details Totally geodesic boundaries of knot complements Totally geodesic boundaries of knot complements

2004-03-25

arxiv.org/abs/math/0403445v2

Mathematics

Geometric Topology

10 pages, no figures, the exposition has been polished, typographical errors corrected, a modicum of detail added, to appear i

Scientific paper

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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