AI 中文总结
研究离散图配置空间，扩展Abrams工作，完全分类简单图所允许的与闭流形同胚的空间，并开发将空间拓扑性质转化为图论性质的技术。
AI 中文摘要
我们研究了2000年Aaron Abrams博士论文中定义的离散图配置空间。具体而言，我们扩展了Abrams的工作，通过完全分类简单图所允许的哪些空间与闭流形同胚。在此过程中，我们开发了将这些空间的拓扑性质转化为图论性质的技术。
英文摘要
We investigate discretized graph configuration spaces as defined by Aaron Abrams in his PhD thesis in 2000. Specifically, we extend Abrams' work by completely classifying which ones admitted by simple graphs are homeomorphic to closed manifolds. In the process of doing so, we develop techniques to translate topological properties of these spaces into graph theoretic ones.
Comments29 pages, 35 figures. This work is based on the second author's Master's Thesis at Ball State University
