CAT(0)-格的收敛与坍缩

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-09-30 DOI:10.1016/j.aim.2025.110555

Nicola Cavallucci , Andrea Sambusetti

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引用次数: 0

摘要

我们研究了CAT(0)-格（即群Γ几何作用于固有的、测地线完备的CAT(0)-空间）及其商（CAT(0)-轨道空间）的收敛性理论。我们描述了一些分裂和坍缩现象，精确地解释了这些作用如何退化为可能的非离散极限作用，并证明了紧CAT(0)-同调轨道的紧性定理。最后，作为该理论的一个应用，我们证明了平面轨道空间的一个隔离结果和一个熵捏定理。

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Convergence and collapsing of CAT(0)-lattices

We study the theory of convergence for CAT(0)-lattices (that is groups Γ acting geometrically on proper, geodesically complete CAT(0)-spaces) and their quotients (CAT(0)-orbispaces). We describe some splitting and collapsing phenomena, explaining precisely how the actions can degenerate to a possibly non-discrete limit action, and prove a compactness theorem for the class of compact CAT(0)-homology orbifolds. Finally, as an application of this theory, we prove an isolation result for flat orbispaces and an entropy-pinching theorem.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.