A complex for right-angled Coxeter groups
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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
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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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2305-2311
- MSC (2000): Primary 20F55; Secondary 05C25, 20F65, 57M20
- DOI: https://doi.org/10.1090/S0002-9939-02-06774-6
- MathSciNet review: 1974626