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

Farber, Michael¹ ; Hanbury, Elizabeth¹

¹Department of Mathematics, University of Durham, South Road, Durham DH1 3LE, UK

Algebraic and Geometric Topology, Tome 10 (2010) no. 4, pp. 2203-2227

Résumé

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.

Détail

DOI : 10.2140/agt.2010.10.2203

Keywords: configuration space, graph, deleted product, homology

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