Algebraic & Geometric Topology 10 (2010) 2203–2227

DOI: 10.2140/agt.2010.10.2203

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.

Keywords

configuration space, graph, deleted product, homology

Mathematical Subject Classification

Primary: 55R80, 57M15

References

Publication

Received: 18 December 2009
Revised: 10 September 2010
Accepted: 13 September 2010
Published: 30 October 2010

Authors