Totally geodesic boundaries of knot complements
classification
🧮 math.GT
keywords
boundarygeodesichyperbolicknottotallywhoseadmitsboundaries
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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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