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The complement of the figure-eight knot geometrically bounds


Author: Leone Slavich
Journal: Proc. Amer. Math. Soc. 145 (2017), 1275-1285
MSC (2010): Primary 51M10, 51M15, 51M20, 52B11
DOI: https://doi.org/10.1090/proc/13272
Published electronically: August 30, 2016
MathSciNet review: 3589325
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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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Additional Information

Leone Slavich
Affiliation: Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
Email: leone.slavich@gmail.com

DOI: https://doi.org/10.1090/proc/13272
Received by editor(s): February 3, 2016
Received by editor(s) in revised form: February 18, 2016, and May 2, 2016
Published electronically: August 30, 2016
Communicated by: David Futer
Article copyright: © Copyright 2016 American Mathematical Society