On knot complements that decompose into regular ideal dodecahedra
On knot complements that decompose into regular ideal dodecahedra
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分解成正则理想十二面体的结补体
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Neil R. Hoffman
中科院分区：
文献类型：
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作者：
Neil R. Hoffman
艾奇逊和鲁宾斯坦指出，有两种截然不同的方法来识别一对正理想十二面体的面并获得结补。本文证明了这些结补是唯一能分解成$$n$$ n个正则理想十二面体的结补，并给出了Neumann和Reid猜想的部分解。主要定理分类的一个推论是双曲结补可以分解为正则理想多面体。
Aitchison and Rubinstein showed there are two distinct ways to identify the faces of a pair of regular ideal dodecahedra and obtain a knot complement. This paper shows that these knot complements are the only knot complements that decompose into $$n$$n regular ideal dodecahedra, providing a partial solution to a conjecture of Neumann and Reid. A corollary of the main theorem classifies the hyperbolic knot complements can be decomposed into regular ideal polyhedra.