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A complex for right-angled Coxeter groups

Author(s): Carl Droms
Journal: Proc. Amer. Math. Soc. 131 (2003), 2305-2311.
MSC (2000): Primary 20F55; Secondary 05C25, 20F65, 57M20
Posted: November 14, 2002
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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:

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
3.: G. P. Scott, Finitely generated 3-manifold groups are finitely presented, J. London Math. Soc. 6 (1973), 437-440. MR 52:1660

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Additional Information:

Carl Droms
Affiliation: Department of Mathematics and Statistics, James Madison University, Harrisonburg, Virginia 22807
Email: carl@math.jmu.edu

DOI: 10.1090/S0002-9939-02-06774-6
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
Posted: November 14, 2002
Communicated by: Stephen D. Smith
Copyright of article: Copyright 2002, American Mathematical Society


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