Labelled oriented graph groups and crossed modules

Nicholas David Gilbert

doi:10.1007/s00013-016-1013-0

Labelled oriented graph groups and crossed modules

Nicholas David Gilbert

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Abstract

A labelled oriented graph (LOG) group is a group given by a presentation constructed in a certain way from a labelled oriented graph: examples include Wirtinger presentations of knot groups. We show how to obtain generators for the Schur Multiplier H₂(G) of a LOG group from the underlying LOG, and by exhibiting the n-string braid group B_n as a LOG group, we compute H₂(B_n).

Original language	English
Pages (from-to)	365–371
Number of pages	7
Journal	Archiv der Mathematik
Volume	108
Issue number	4
Early online date	10 Jan 2017
DOIs	https://doi.org/10.1007/s00013-016-1013-0
Publication status	Published - Apr 2017

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This is a post-peer-review, pre-copyedit version of an article published in Archiv der Mathematik. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00013-016-1013-0
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Nick Gilbert
- N.D.Gilberthw.acuk
- School of Mathematical & Computer Sciences - Professor
- School of Mathematical & Computer Sciences, Mathematics - Professor
Person: Academic (Research & Teaching)

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title = "Labelled oriented graph groups and crossed modules",

abstract = "A labelled oriented graph (LOG) group is a group given by a presentation constructed in a certain way from a labelled oriented graph: examples include Wirtinger presentations of knot groups. We show how to obtain generators for the Schur Multiplier H2(G) of a LOG group from the underlying LOG, and by exhibiting the n-string braid group Bn as a LOG group, we compute H2(Bn).",

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DO - 10.1007/s00013-016-1013-0

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Labelled oriented graph groups and crossed modules

Abstract

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Nick Gilbert

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