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

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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Keywords

configuration space, graph, deleted product, homology

Mathematical Subject Classification 2000

Primary: 55R80, 57M15

References

Publication

Received: 18 December 2009

Revised: 10 September 2010

Accepted: 13 September 2010

Published: 30 October 2010

Authors

Michael Farber
Department of Mathematics University of Durham South Road Durham DH1 3LE UK
http://maths.dur.ac.uk/~dma0mf/
Elizabeth Hanbury
Department of Mathematics University of Durham South Road Durham DH1 3LE UK

Volume 10, issue 4 (2010)

Michael Farber and Elizabeth Hanbury

Abstract