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arXiv · 1005.2300

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

Michael Farber·Elizabeth Hanbury
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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.

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Michael Farber, Elizabeth Hanbury. 2010-10-25. Topology of configuration space of two particles on a graph, II. https://doi.org/10.2140/agt.2010.10.2203

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