Cross Ratios, Surface Groups, SL(n, R) and
Cross Ratios, Surface Groups, SL(n, R) and
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交叉比、表面组、SL(n, R) 和
DOI：
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发表时间：
2008
期刊：
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通讯作者：
F. Labourie
中科院分区：
文献类型：
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作者：
F. Labourie
我们在本文中介绍了交叉比和表面基团表示之间的关系。更具体地说，我们将表示的连通分量描述为 SL(n, R) 作为群无穷远边界上的交比集，满足一些取决于 n 的函数关系。我们还表明，C(S) ⋊ Diff(S) 的表示可以描述为交叉比率。我们展示了这种表征的“性格多样性”。我们证明该特征簇包含 SL(n, R) 的所有特征簇以及表面上所有负弯曲度量的集合。
We present in this article relations between cross ratios and representations of surface groups. More specifically, we describe a connected component of representations into SL(n, R) as the set of cross ratios on the boundary at infinity of the group which satisfy some functional relations depending on n. We also show that representations into C(S) ⋊ Diff(S) can be described as cross ratios. We exhibit a ”character variety” of such representations. We show that this character variety contains all character varieties for SL(n, R) as well as the set of all negatively curved metrics on the surface.