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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Right-angled mock reflection and mock Artin groups


Author: Richard Scott
Journal: Trans. Amer. Math. Soc. 360 (2008), 4189-4210
MSC (2000): Primary 20Fxx
Published electronically: March 12, 2008
MathSciNet review: 2395169
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Abstract: We define a right-angled mock reflection group to be a group $ G$ acting combinatorially on a CAT(0) cubical complex such that the action is simply-transitive on the vertex set and all edge-stabilizers are $ \mathbb{Z}_2$. We give a combinatorial characterization of these groups in terms of graphs with local involutions. Any such graph $ \Gamma$ not only determines a mock reflection group, but it also determines a right-angled mock Artin group. Both classes of groups generalize the corresponding classes of right-angled Coxeter and Artin groups. We conclude by showing that the standard construction of a finite $ K(\pi,1)$ space for right-angled Artin groups generalizes to these mock Artin groups.


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Additional Information

Richard Scott
Affiliation: Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, California 95053
Email: rscott@math.scu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04452-8
PII: S 0002-9947(08)04452-8
Received by editor(s): June 26, 2006
Published electronically: March 12, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.