GRAPH BRAID GROUPS AND RIGHT-ANGLED ARTIN GROUPS

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We give a necessary and sufficient condition for a graph to have a right-angled Artin group as its braid group for braid index >= 5. In order to have the necessity part, graphs are organized into small classes so that one of the homological or cohomological characteristics of right-angled Artin groups can be applied. Finally we show that a given graph is planar if the first homology of its 2-braid group is torsion-free, and we leave the corresponding statement for n-braid groups as a conjecture along with a few other conjectures about graphs whose braid groups of index <= 4 are right-angled Artin groups.
Publisher
AMER MATHEMATICAL SOC
Issue Date
2012-01
Language
English
Article Type
Article
Keywords

MORSE-THEORY

Citation

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.364, no.1, pp.309 - 360

ISSN
0002-9947
URI
http://hdl.handle.net/10203/96985
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
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