Topology of configuration space of two particles on a graph, II
Algebraic Topology
2015-03-17 v2 Combinatorics
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
Cite
@article{arxiv.1005.2300,
title = {Topology of configuration space of two particles on a graph, II},
author = {Michael Farber and Elizabeth Hanbury},
journal= {arXiv preprint arXiv:1005.2300},
year = {2015}
}
Comments
24 pages, 12 figures; Section 7 revised in v2, published version