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 \(H_2(G)\) of a LOG group from the underlying LOG, and by exhibiting the n-string braid group \(B_n\) as a LOG group, we compute \(H_2(B_n)\).
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The author is grateful to Jim Howie for his insightful comments on this work and for his skill in drawing illuminating spherical diagrams. The author also thanks the perspicacious referee for several suggestions that improved the exposition, both grammatically and mathematically.
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Gilbert, N.D. Labelled oriented graph groups and crossed modules. Arch. Math. 108, 365–371 (2017). https://doi.org/10.1007/s00013-016-1013-0
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DOI: https://doi.org/10.1007/s00013-016-1013-0