The complement of the figure-eight knot geometrically bounds

Slavich, Leone

doi:10.1090/proc/13272

The complement of the figure-eight knot geometrically bounds
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Proc. Amer. Math. Soc. 145 (2017), 1275-1285 Request permission

Abstract:

We show that some hyperbolic $3$-manifolds which are tessellated by copies of the regular ideal hyperbolic tetrahedron are geodesically embedded 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 is the first example of geometrically bounding hyperbolic knot complements and, amongst known examples of geometrically bounding manifolds, the one with the smallest volume.

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