平方复形与单纯非正曲率
Square complexes and simplicial nonpositive curvature
摘要：
我们证明了每个非正曲方形VH-复形都可以函化为同伦型的局部6-大单纯复形。因此，任何几何作用于CAT（0）平方VH-复形的群都是收缩的。特别地，两个双生成的自由群的乘积是收缩的，这回答了Daniel Wise的一个问题。另一方面，我们展示了一个例子，紧凑的非VH非正弯曲的平方复杂，其基本群既不是收缩，也不是几乎收缩。
英文摘要：
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 geometrically 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 compact non-VH nonpositively curved square complex, whose fundamental group is neither systolic, nor even virtually systolic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
