On the second homology of planar graph braid groups

Abstract

We show that the second homology of the configuration spaces of a planar graph is generated under the operations of embedding, disjoint union, and edge stabilization by three atomic graphs: the cycle graph with one edge, the star graph with three edges, and the theta graph with four edges. We give an example of a non-planar graph for which this statement is false.

arXiv comment24 pages, 17 figures. To appear in the Journal of Topology. May differ slightly from published version