政治结构与单纯复形拓扑
Political structures and the topology of simplicial complexes
摘要：
我们使用单纯复形的拓扑来模拟政治结构[1]。单纯形复合体是一种自然的工具，以编码的结构中的相互作用，因为一个单纯形可以用来表示一个子集的兼容代理。我们翻译成语言的政治结构的楔形，圆锥体，和暂停操作，并显示这些建设如何对应于合并结构和引入调解人。我们介绍了一个代理的可行性和政治系统的稳定性的概念，并检查它们的相互作用与单纯复杂的拓扑结构，铸造他们的相互作用在范畴理论的语言只要有可能。我们引入了一个改进的模型，通过分配权重对应的问题的代理agreeon. Also，单纯形复合体的同源性的数量来检测非活力，某些周期的不相容剂，和（非）存在的调解人。最后，我们推广了[1]的一些结果，将生存性和稳定性引入到友好代表的语言中，并使用同调来研究R-妥协和D-妥协的存在性。
英文摘要：
We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible agents. We translate the wedge, cone, and suspension operations into the language of political structures and show how these constructions correspond to merging structures and introducing mediators. We introduce the notions of the viability of an agent and the stability of a political system and examine their interplay with the simplicial complex topology, casting their interactions in category-theoretic language whenever possible. We introduce a refinement of the model by assigning weights to simplices corresponding to the number of issues the agents agree on. In addition, homology of simplicial complexes is used to detect non-viabilities, certain cycles of incompatible agents, and the (non)presence of mediators. Finally, we extend some results from [1], bringing viability and stability into the language of friendly delegations and using homology to examine the existence of R-compromises and D-compromises.
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