On the second homology of planar graph braid groups
Algebraic Topology
2022-02-02 v2 Geometric Topology
Abstract
We show that the second homology of the configuration spaces of a planar graph is generated under the operations of embedding, disjoint union, and edge stabilization by three atomic graphs: the cycle graph with one edge, the star graph with three edges, and the theta graph with four edges. We give an example of a non-planar graph for which this statement is false.
Keywords
Cite
@article{arxiv.2008.10371,
title = {On the second homology of planar graph braid groups},
author = {Byung Hee An and Ben Knudsen},
journal= {arXiv preprint arXiv:2008.10371},
year = {2022}
}
Comments
24 pages, 17 figures. To appear in the Journal of Topology. May differ slightly from published version