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arXiv · 1511.08684

The complement of the figure-eight knot geometrically bounds

Leone Slavich
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Abstract

We show that some hyperbolic 3-manifolds which are tessellated by copies of the regular ideal hyperbolic tetrahedron embed geodesically in a complete, finite volume, hyperbolic 4-manifold. This allows us to prove that the complement of the figure-eight knot geometrically bounds a complete, finite volume hyperbolic 4-manifold. This the first example of geometrically bounding hyperbolic knot complement and, amongst known examples of geometrically bounding manifolds, the one with the smallest volume.

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Leone Slavich. 2016-07-27. The complement of the figure-eight knot geometrically bounds. https://doi.org/10.1090/proc%2F13272

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