论文标题
半简单谎言群体的共同体学，从无穷大看
The cohomology of semi-simple Lie groups, viewed from infinity
论文作者
论文摘要
我们证明，半简单谎言群的共同体学允许边界值，这些边界值是弗斯滕贝格边界上可测量的共生。这将概括为已知的不变性，例如Shilov边界上的Maslov索引，投影空间上的Euler类或球体上的双曲理想体积。 在第一个等级中，这导致了该组和该边界模型的同构之间的同构。在较高的等级中，出现其他类别，我们将完全确定。
We prove that the cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on projective space, or the hyperbolic ideal volume on spheres. In rank one, this leads to an isomorphism between the cohomology of the group and of this boundary model. In higher rank, additional classes appear, which we determine completely.
