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Topology of configuration space of two particles on a graph, {II}

Michael Farber and Elizabeth Hanbury

Algebraic & Geometric Topology 10 (2010) 2203–2227

This paper continues the investigation of the configuration space of two distinct points on a graph. We analyze the process of adding an additional edge to the graph and the resulting changes in the topology of the configuration space. We introduce a linking bilinear form on the homology group of the graph with values in the cokernel of the intersection form (introduced in Part I of this work). For a large class of graphs, which we call mature graphs, we give explicit expressions for the homology groups of the configuration space. We show that under a simple condition, adding an edge to a mature graph yields another mature graph.

configuration space, graph, deleted product, homology
Mathematical Subject Classification 2000
Primary: 55R80, 57M15
Received: 18 December 2009
Revised: 10 September 2010
Accepted: 13 September 2010
Published: 30 October 2010
Michael Farber
Department of Mathematics
University of Durham
South Road
Durham DH1 3LE
Elizabeth Hanbury
Department of Mathematics
University of Durham
South Road
Durham DH1 3LE