泛树分次空间与渐近锥面
Universal tree-graded spaces and asymptotic cones
摘要：
我们定义并给出了明确的建设的普遍树分次空间与一个给定的收集件。我们应用这一点来证明相对双曲群的渐近锥面的唯一性，相对双曲群的外围子群具有唯一的渐近锥面。在模连续统假设下，证明了若测地线度量空间的一个渐近锥面是齐次的且有割点，则它是泛树分次空间，其中有片极大连通子集而没有它们自己的割点.因此，它完全取决于它的作品集。
英文摘要：
We define and give explicit construction of the universal tree-graded space with a given collection of pieces. We apply that to proving uniqueness of asymptotic cones of relatively hyperbolic groups whose peripheral subgroups have unique asymptotic cones. Modulo the Continuum Hypothesis, we show that if an asymptotic cone of a geodesic metric space is homogeneous and has cut points, then it is the universal tree-graded space with pieces - maximal connected subsets without their own cut points. Thus it is completely determined by its collection of pieces.
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