Let $X=G/K$ be a higher rank symmetric space of non-compact type, where $G$is the connected component of the isometry group of $X$. We define thesplitting rank of $X$, denoted by $\text{srk}(X)$, to be the maximal dimensionof a totally geodesic submanifold $Y\subset X$ which splits off an isometric$\mathbb R$-factor. We compute explicitly the splitting rank for eachirreducible symmetric space. For an arbitrary (not necessarily irreducible)symmetric space, we show that the comparison map$\eta:H^{*}_{c,b}(G,\mathbb{R})\rightarrow H^{*}_c(G,\mathbb{R})$ is surjectivein degrees $*\geq \text{srk}(X)+2$, provided $X$ has no small direct factors.
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机译：令$ X = G / K $为非紧实类型的更高阶对称空间，其中$ G $是$ X $等轴测图组的连接组件。我们将以$ \ text {srk}（X）$表示的$ X $的分解等级定义为完全测地子流形$ Y \子集X $的最大尺寸，该子流形将等距$ \ mathbb R $因子分开。我们显式计算每个不可约对称空间的分裂秩。对于任意（不一定是不可约）对称空间，我们证明比较图$ \ eta：H ^ {*} _ {c，b}（G，\ mathbb {R}）\ rightarrow H ^ {*} _ c（ G，\ mathbb {R}）$是形容词度$ * \ geq \ text {srk}（X）+ 2 $，前提是$ X $没有小的直接因子。
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