Abstract
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.
Citation
Michael Farber. Elizabeth Hanbury. "Topology of configuration space of two particles on a graph, {II}." Algebr. Geom. Topol. 10 (4) 2203 - 2227, 2010. https://doi.org/10.2140/agt.2010.10.2203
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