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(Γ,2) of two distinct particles on a graph Γ. Our main tool is intersection theory for cycles in graphs. We obtain an explicit description of the cohomology algebra H(F(Γ,2);Q) in the case of planar graphs.

Keywords
configuration space, graph, planar graph, deleted product, cohomology
Mathematical Subject Classification 2000
Primary: 55R80
Secondary: 57M15
References
Publication
Received: 24 November 2008
Revised: 28 February 2009
Accepted: 7 March 2009
Published: 30 March 2009
Authors
Kathryn Barnett
Department of Mathematics
University of Durham
Durham DH1 3LE
UK
Michael Farber
Department of Mathematics
University of Durham
Durham DH1 3LE
UK
http://maths.dur.ac.uk/~dma0mf/