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.; 2/ 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 H .F.; 2/I Q/ in the case of planar graphs. 55R80; 57M15 Let F.X; n/ denote the space of configurations of n distinct points lying in a topological space X , ie F.X; n/ D f.x 1 ; x 2 ; : : : ; x n / 2 X X I x i 6 D x j for i 6 D j g: