Volume 9, issue 1 (2009)

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

Kathryn Barnett and Michael Farber

Algebraic & Geometric Topology 9 (2009) 593–624
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.

Keywords
configuration space, graph, planar graph, deleted product, cohomology
Primary: 55R80
Secondary: 57M15