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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
MathSciNet review:
1974626
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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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