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

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

2 Citations (Scopus)

100 Downloads (Pure)

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

Access to Document

10.1007/s00013-016-1013-0

Download pdf
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
Accepted author manuscript, 260 KB

Cite this

@article{ff988d7a0ff241e29aba89d05dd7524c,

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).",

author = "Gilbert, {Nicholas David}",

year = "2017",

month = apr,

doi = "10.1007/s00013-016-1013-0",

language = "English",

volume = "108",

pages = "365–371",

journal = "Archiv der Mathematik",

issn = "0003-889X",

publisher = "Birkh{\"a}user",

number = "4",

}

TY - JOUR

T1 - Labelled oriented graph groups and crossed modules

AU - Gilbert, Nicholas David

PY - 2017/4

Y1 - 2017/4

N2 - 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).

AB - 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).

U2 - 10.1007/s00013-016-1013-0

DO - 10.1007/s00013-016-1013-0

M3 - Article

SN - 0003-889X

VL - 108

SP - 365

EP - 371

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 4

ER -

Labelled oriented graph groups and crossed modules

Abstract

Access to Document

Fingerprint

Cite this