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Topology of configuration space of two particles on a graph, II
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Farber, Michael and Hanbury, Elizabeth (2010) Topology of configuration space of two particles on a graph, II. Algebraic & Geometric Topology, Vol.10 (No.4). pp. 2203-2227. doi:10.2140/agt.2010.10.2203 ISSN 1472-2747.
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Official URL: http://dx.doi.org/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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Algebraic & Geometric Topology | ||||
Publisher: | Mathematical Sciences Publishers | ||||
ISSN: | 1472-2747 | ||||
Official Date: | 30 October 2010 | ||||
Dates: |
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Volume: | Vol.10 | ||||
Number: | No.4 | ||||
Page Range: | pp. 2203-2227 | ||||
DOI: | 10.2140/agt.2010.10.2203 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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