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

Farber, Michael; Hanbury, Elizabeth

doi:10.2140/agt.2010.10.2203

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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

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 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)