Volume 10, issue 4 (2010)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Topology of configuration space of two particles on a graph, {II}

Michael Farber and Elizabeth Hanbury

Algebraic & Geometric Topology 10 (2010) 2203–2227
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 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