Hyperbolic Structures on the Configuration Space of Six Points in the Projective Line
Hyperbolic Structures on the Configuration Space of Six Points in the Projective Line
复制标题
射影线六点位形空间上的双曲结构
DOI：
10.1006/aima.1999.1840
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
Haruko Nishi
中科院分区：
文献类型：
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作者：
B. Morin;Haruko Nishi
实射影线上六点的定向构型空间X+6是一个非紧三维流形，它具有独特的十尖点有限体积完全双曲结构。另一方面，它自然分解为 120 个单元，每个单元可以解释为单位面积的等角六边形的集合。类似的双曲结构可以通过考虑非等角六边形来获得，使得X+6上的标准双曲结构位于有限体积双曲结构的五参数族的中心。本文有助于研究该家族的特性。特别是，我们展示了从一组规定的六边形角度到 R10 的真实解析图，其分量是十个尖点处的单峰轨迹。我们表明这张地图的中心最高排名为 5。
The oriented configuration space X+6 of six points on the real projective line is a noncompact three-dimensional manifold which admits a unique complete hyperbolic structure of finite volume with ten cusps. On the other hand, it decomposes naturally into 120 cells each of which can be interpreted as the set of equiangular hexagons with unit area. Similar hyperbolic structures can be obtained by considering nonequiangular hexagons so that the standard hyperbolic structure on X+6 is at the center of a five parameter family of hyperbolic structures of finite volume. This paper contributes to investigations of the properties of this family. In particular, we exhibit two real analytic maps from the set of prescribed angles of hexagons into R10 whose components are the traces of the monodromies at the ten cusps. We show that this map has maximal rank 5 at the center.