1. The complement of the figure-eight knot geometrically bounds
- Author
-
Slavich, Leone
- Subjects
Mathematics - Geometric Topology ,Mathematics - Combinatorics ,Mathematics - Metric Geometry ,51M10, 51M15, 51M20, 52B11 - 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., Comment: 9 pages, 4 figures, typos corrected, improved exposition of tetrahedral manifolds. Added Proposition 3.3, which gives necessary and sufficient conditions for M_T to be a manifold, and Remark 4.4, which shows that the figure-eight knot bounds a 4-manifold of minimal volume. Updated bibliography
- Published
- 2015
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