Graph braid groups and right-angled Artin groups
Authors:
Jee Hyoun Kim, Ki Hyoung Ko and Hyo Won Park
Journal:
Trans. Amer. Math. Soc. 364 (2012), 309-360
MSC (2010):
Primary 20F36, 20F65, 57M15
DOI:
https://doi.org/10.1090/S0002-9947-2011-05399-7
Published electronically:
August 2, 2011
MathSciNet review:
2833585
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We give a necessary and sufficient condition for a graph to have a right-angled Artin group as its braid group for braid index . 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 iff the first homology of its 2-braid group is torsion-free, and we leave the corresponding statement for
-braid groups as a conjecture along with a few other conjectures about graphs whose braid groups of index
are right-angled Artin groups.
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Additional Information
Jee Hyoun Kim
Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Korea
Email:
kimjeehyoun@kaist.ac.kr
Ki Hyoung Ko
Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Korea
Email:
knot@kaist.ac.kr
Hyo Won Park
Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Korea
Email:
H.W.Park@kaist.ac.kr
DOI:
https://doi.org/10.1090/S0002-9947-2011-05399-7
Keywords:
Braid group,
right-angled Artin group,
discrete Morse theory,
planar,
graph
Received by editor(s):
August 11, 2009
Received by editor(s) in revised form:
May 24, 2010, June 6, 2010, and June 12, 2010
Published electronically:
August 2, 2011
Additional Notes:
This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (No. R01-2006-000-10152-0)
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.