八字形纽结的补空间在几何上界定
几何拓扑
2019-10-22 v4 组合数学
度量几何
摘要
我们展示了一些由正则理想双曲四面体副本镶嵌的双曲3-流形，测地嵌入到一个完备、有限体积的双曲4-流形中。这使我们能够证明八字形纽结的补空间在几何上界定一个完备、有限体积的双曲4-流形。这是几何界定双曲纽结补的第一个例子，并且在已知几何界定流形的例子中，是体积最小的一个。
引用
@article{arxiv.1511.08684,
title = {The complement of the figure-eight knot geometrically bounds},
author = {Leone Slavich},
journal= {arXiv preprint arXiv:1511.08684},
year = {2019}
}
备注
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