SLn（R）Cartan次群空间的压缩
Compactification de Chabauty de l'espace des sous-groupes de Cartan de SLn(R)
摘要：
设G是一个具有有限中心、有限连通分支数且无紧因子的实半单李群。我们感兴趣的是G的Cartan子群的齐性空间，它也可以看作是G的对称空间的极大平坦空间。我们定义它的Chabauty紧化为G的闭子群空间中的闭包，并赋予其Chabauty拓扑.证明了当G的实秩为1时，或当G= SL 3（R）或SL 4（R）时，此紧化是G的实秩维的所有闭连通交换子群的集合，且具有实谱.在SL 3（R）的情形下，我们更仔细地研究了它的拓扑，证明了它是单连通的.
英文摘要：
Let G be a real semisimple Lie group with finite center, with a finite number of connected components and without compact factor. We are interested in the homogeneous space of Cartan subgroups of G, which can be also seen as the space of maximal flats of the symmetric space of G. We define its Chabauty compactification as the closure in the space of closed subgroups of G, endowed with the Chabauty topology. We show that when the real rank of G is 1, or when G=SL3(R) or SL4(R), this compactification is the set of all closed connected abelian subgroups of dimension the real rank of G, with real spectrum. And in the case of SL3(R), we study its topology more closely and we show that it is simply connected.
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