In this paper we study the homology and cohomology of configuration spaces of two distinct particles on a graph . Our main tool is intersection theory for cycles in graphs. We obtain an explicit description of the cohomology algebra in the case of planar graphs.
"Topology of configuration space of two particles on a graph, I." Algebr. Geom. Topol. 9 (1) 593 - 624, 2009. https://doi.org/10.2140/agt.2009.9.593