This paper accomplishes two things. First, we construct a geometric analog of the rational Tits building for general noncompact, complete, finite volume n-manifolds M of bounded nonpositive curvature. Second, we prove that this analog has dimension less than \(\lfloor n/2\rfloor \).

中文翻译：

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非正曲率流形末端的半维塌陷

本文完成了两件事。首先，我们为有界非正曲率的一般非紧致的，完整的，有限体积的n流形M构造有理Tits建筑物的几何类似物。其次，我们证明该类似物的尺寸小于\（\ lfloor n / 2 \ rfloor \）。