We consider, for a finite graph G, when the surjective map ${\mathrm{Conf}}_{n+1}(G)\to {\mathrm{Conf}}_n(G)$ of configuration spaces admits a section. We study when the answer depends only on the homotopy type of G, and give a complete answer. We also provide basic techniques for construction of sections.

中文翻译：

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图配置空间的截面问题

我们考虑，对于有限图G，当满射映射${\mathrm{会议}}_{n+1}(G)\to {\mathrm{会议}}_n(G)$的配置空间承认一个部分。我们研究何时答案仅取决于G的同伦类型，并给出完整答案。我们还提供构建截面的基本技术。