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


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. "Topology of configuration space of two particles on a graph, {II}." Algebr. Geom. Topol. 10 (4) 2203 - 2227, 2010.


Received: 18 December 2009; Revised: 10 September 2010; Accepted: 13 September 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1215.55006
MathSciNet: MR2745669
Digital Object Identifier: 10.2140/agt.2010.10.2203

Primary: 55R80 , 57M15

Keywords: configuration space , deleted product , graph , homology

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.10 • No. 4 • 2010
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