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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A complex for right-angled Coxeter groups

Author: Carl Droms
Journal: Proc. Amer. Math. Soc. 131 (2003), 2305-2311
MSC (2000): Primary 20F55; Secondary 05C25, 20F65, 57M20
Published electronically: November 14, 2002
MathSciNet review: 1974626
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Abstract | References | Similar Articles | Additional Information

Abstract: We associate to each right-angled Coxeter group a 2-dimensional complex. Using this complex, we show that if the presentation graph of the group is planar, then the group has a subgroup of finite index which is a 3-manifold group (that is, the group is virtually a 3-manifold group). We also give an example of a right-angled Coxeter group which is not virtually a 3-manifold group.

References [Enhancements On Off] (What's this?)

  • 1. H. Servatius, C. Droms and B. Servatius, Surface subgroups of graph groups, Proc. Amer. Math. Soc. 106 (1989), 573-578. MR 90f:20052
  • 2. J. Stallings, Coherence of 3-manifold fundamental groups, in Séminaire Bourbaki, Vol. 1975/76, 28 ème année, Exp. No. 481, pp. 167-173. Lecture Notes in Math., Vol. 567, Springer, Berlin, 1977. MR 56:1290
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Additional Information

Carl Droms
Affiliation: Department of Mathematics and Statistics, James Madison University, Harrisonburg, Virginia 22807

PII: S 0002-9939(02)06774-6
Keywords: Right-angled Coxeter group, two-dimensional complex, three-manifold group
Received by editor(s): October 31, 2001
Received by editor(s) in revised form: March 10, 2002
Published electronically: November 14, 2002
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2002 American Mathematical Society