Topology of configuration space of two particles on a graph, I

Abstract

In this paper we study the homology and cohomology of configuration spaces $F\left(\Gamma ,2\right)$ of two distinct particles on a graph $\Gamma$. Our main tool is intersection theory for cycles in graphs. We obtain an explicit description of the cohomology algebra $H^{\ast }\left(F\left(\Gamma ,2\right);Q\right)$ in the case of planar graphs.