Section Problems for Graph Configuration Spaces

Abstract

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.

23 pages, 16 figures