On the second homology of planar graph braid groups

Byung Hee An; Ben Knudsen

doi:10.1112/topo.12228

On the second homology of planar graph braid groups

Byung Hee An
, Ben Knudsen

Department of Mathematics Education

Northeastern University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	666-691
Number of pages	26
Journal	Journal of Topology
Volume	15
Issue number	2
DOIs	https://doi.org/10.1112/topo.12228
State	Published - Jun 2022

Keywords

20F36
55R80 (primary)

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10.1112/topo.12228

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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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AB - 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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On the second homology of planar graph braid groups

Abstract

Keywords

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