Volume 10, issue 4 (2010)

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

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

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
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
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