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arXiv · 2008.10371

On the second homology of planar graph braid groups

Byung Hee An·Ben Knudsen
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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.

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Byung Hee An, Ben Knudsen. 2020-08-24. On the second homology of planar graph braid groups. https://arxiv.org/abs/2008.10371

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