发表机构
Pusan National University（釜山国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为弱特殊方形复形定义乘积子复形与交集复形，证明其与万有覆盖的覆叠商典范同构，并建立拟等距诱导交集复形同构的定理。
AI 中文摘要
我们为紧致非正曲率方形复形和CAT(0)方形复形定义了乘积子复形和交集复形。乘积子复形被定义为具有嵌入坐标纤维的图的乘积的局部等距的等价类。利用它们的分解，我们给出了交集复形的统一定义，推广了S. Oh的论文“弱特殊方形复形的拟等距不变量”（Topology and its Applications 307 (2022)）中的构造。立方自同构在这些复形上诱导作用。我们通过比较核心映射标签的相容提升及其沿面链的分解来定义态射。对于紧致双侧弱特殊方形复形，我们证明其交集复形典范同构于其万有覆盖的交集复形的覆叠商。在简单性假设下，这恢复了该论文中由像定义的约化交集复形，并且乘积基群是完全的单纯形稳定子群。我们还证明了紧致双侧弱特殊方形复形的万有覆盖之间的拟等距在该意义下诱导其交集复形的同构，并给出了有限反例，解释为何仅凭像一般不能确定该商。
英文摘要
We define product subcomplexes and intersection complexes for compact nonpositively curved square complexes and CAT(0) square complexes. Product subcomplexes are defined as equivalence classes of local isometries from products of graphs with embedded coordinate fibers. Using their factorizations, we give a common definition of the intersection complex, extending the constructions in S. Oh's paper "Quasi-isometry invariants of weakly special square complexes" (Topology and its Applications 307 (2022)). Cubical automorphisms induce actions on these complexes. We define morphisms by comparing compatible elevations of core-map labels and their factorizations along face chains. For a compact two-sided weakly special square complex, we prove that its intersection complex is canonically isomorphic to the deck quotient of the intersection complex of its universal cover. Under a simplicity hypothesis, this recovers the image-defined reduced intersection complex in that paper, and product-base groups are the full simplex stabilizers. We also prove that quasi-isometries between universal covers of compact two-sided weakly special square complexes induce isomorphisms of their intersection complexes in this sense, and give finite counterexamples explaining why images alone do not determine the quotient in general.
Comments24 pages, 4 figures. Revisits and corrects the constructions of product subcomplexes and intersection complexes in arXiv:2009.03865
