The complement of the figure-eight knot geometrically bounds
The complement of the figure-eight knot geometrically bounds
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DOI：
10.1090/proc/13272
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发表时间：
2015-11
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影响因子：
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通讯作者：
Leone Slavich
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文献类型：
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作者：
Leone Slavich
我们展示了一些由正则理想双曲四面体的副本镶嵌而成的双曲 3 流形，测地线嵌入在完整的、有限体积的双曲 4 流形中。这使我们能够证明 8 字形结的补集在几何上限制了一个完整的有限体积双曲 4 流形。这是几何边界双曲结补的第一个例子，并且是几何边界流形的已知例子中体积最小的一个。
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.