Generalized bipyramids and hyperbolic volumes of alternating k-uniform tiling links
Generalized bipyramids and hyperbolic volumes of alternating k-uniform tiling links
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交替 k-均匀平铺链接的广义双锥体和双曲体积
DOI：
10.1016/j.topol.2019.107045
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发表时间：
2017
影响因子：
0.6
通讯作者：
Nathaniel Mayer
中科院分区：
文献类型：
--
作者：
C. Adams;Aaron Calderon;Nathaniel Mayer
我们给出了交替k-均匀平铺连接的双曲补的显式几何分解，这些交替连接的投影图是s2， e2或h2的k-均匀平铺。这种分解的结果是，球面交替k-均匀平铺连杆的体积恰好是相同组合描述的理想阿基米德固体的最大体积的两倍，双曲交替平铺连杆的双曲结构来自H 2上k-均匀平铺的等边实现。在双曲平铺连杆的情况下，我们被引入考虑嵌入在加厚曲面S gx I中且属g≥2和完全测地线边界的连杆。我们将Adams的双锥体构造推广到截断双锥体，并利用它们证明了S gx I中所有g≥2的双曲连杆的可能体积密度集是区间[0,2 v oct]的密集子集，其中v oct≈3.66386为理想正八面体的体积。
We present explicit geometric decompositions of the hyperbolic complements of alternating k-uniform tiling links, which are alternating links whose projection graphs are k-uniform tilings of S 2, E 2, or H 2. A consequence of this decomposition is that the volumes of spherical alternating k-uniform tiling links are precisely twice the maximal volumes of the ideal Archimedean solids of the same combinatorial description, and the hyperbolic structures for the hyperbolic alternating tiling links come from the equilateral realization of the k-uniform tiling on H 2. In the case of hyperbolic tiling links, we are led to consider links embedded in thickened surfaces S g× I with genus g≥ 2 and totally geodesic boundaries. We generalize the bipyramid construction of Adams to truncated bipyramids and use them to prove that the set of possible volume densities for all hyperbolic links in S g× I, ranging over all g≥ 2, is a dense subset of the interval [0, 2 v oct], where v oct≈ 3.66386 is the volume of the ideal regular octahedron.
影响因子：
0.7
作者：
.Ilker S. Yuce-Ilker-S.-Yuce-102800584
通讯作者：
.Ilker S. Yuce-Ilker-S.-Yuce-102800584
加厚表面链接的双曲性
影响因子：
0.6
作者：
Adams, C.;Albors-Riera, C.;Haddock, B.;Li, Z.;Nishida, D.;Reinoso, B.;Wang, L.
通讯作者：
Wang, L.