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

Barnett, Kathryn; Farber, Michael

doi:10.2140/agt.2009.9.593

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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

DOI: 10.2140/agt.2009.9.593

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/

Volume 9, issue 1 (2009)