论文标题
可收缩的，双曲线但非猫（0）配合物
Contractible, hyperbolic but non-CAT(0) complexes
论文作者
论文摘要
我们证明，几乎所有的ARC复合物都不容纳具有有限形状有限的CAT（0）度量，尤其是映射类组的任何有限索引子组都不会在ARC复合物上保留这样的度量。我们还显示了除了有限的许多碟片复合物和自由分裂组的圆盘复合物外，我们还显示了类似的陈述。阻塞是组合的。这些复合物都是双曲线和可收缩的，但是尽管如此，我们表明它们不满足组合等等级不平等：对于任何n，有一个长度为4的环，仅限制了至少由n个三角形组成的圆盘。 另一方面，我们表明曲线络合物满足了线性组合等级不平等，这回答了安德鲁·普特曼（Andrew Putman）的问题。
We prove that almost all arc complexes do not admit a CAT(0) metric with finitely many shapes, in particular any finite-index subgroup of the mapping class group does not preserve such a metric on the arc complex. We also show the analogous statement for all but finitely many disc complexes of handlebodies and free splitting complexes of free groups. The obstruction is combinatorial. These complexes are all hyperbolic and contractible but despite this we show that they satisfy no combinatorial isoperimetric inequality: for any n there is a loop of length 4 that only bounds discs consisting of at least n triangles. On the other hand we show that the curve complexes satisfy a linear combinatorial isoperimetric inequality, which answers a question of Andrew Putman.
