Square complexes and simplicial nonpositive curvature
Square complexes and simplicial nonpositive curvature
复制标题
平方复形和单纯非正曲率
DOI：
10.1090/s0002-9939-2013-11568-6
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发表时间：
2011
影响因子：
2
通讯作者：
P. Przytycki
中科院分区：
文献类型：
--
作者：
Tomasz Elsner;P. Przytycki
我们证明了每个非正曲的平方VH复形都可以函化为同一同伦类型的局部6-大单纯复形。由此可见，任何适当地作用于CAT（0）平方VH-复形上的群都是收缩的。特别地，两个自由群的乘积是收缩的，这回答了丹尼尔怀斯的一个问题。另一方面，我们展示了一个例子，一个非VH nonpositively弯曲的平方复杂的基本组既不是收缩，甚至几乎收缩。
We prove that each nonpositively curved square VH-complex can be turned functorially into a locally 6-large simplicial complex of the same homotopy type. It follows that any group acting properly and cocompactly on a CAT(0) square VH-complex is systolic. In particular, the product of two finitely generated free groups is systolic, which answers a question of Daniel Wise. On the other hand, we exhibit an example of a non-VH nonpositively curved square complex whose fundamental group is neither systolic nor even virtually systolic.