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

2 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)

Access to Document

10.1112/topo.12228

Cite this

@article{25bca0d71a024ce5994a9687d40cc6a9,

title = "On the second homology of planar graph braid groups",

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 = "20F36, 55R80 (primary)",

author = "An, {Byung Hee} and Ben Knudsen",

note = "Publisher Copyright: {\textcopyright} 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.",

year = "2022",

month = jun,

doi = "10.1112/topo.12228",

language = "English",

volume = "15",

pages = "666--691",

journal = "Journal of Topology",

issn = "1753-8416",

publisher = "John Wiley and Sons Ltd",

number = "2",

}

TY - JOUR

T1 - On the second homology of planar graph braid groups

AU - An, Byung Hee

AU - Knudsen, Ben

PY - 2022/6

Y1 - 2022/6

N2 - 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.

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.

KW - 20F36

KW - 55R80 (primary)

UR - http://www.scopus.com/inward/record.url?scp=85132559385&partnerID=8YFLogxK

U2 - 10.1112/topo.12228

DO - 10.1112/topo.12228

M3 - Article

AN - SCOPUS:85132559385

SN - 1753-8416

VL - 15

SP - 666

EP - 691

JO - Journal of Topology

JF - Journal of Topology

IS - 2

ER -

On the second homology of planar graph braid groups

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this