Incoherent Coxeter Groups
Authors:
Kasia Jankiewicz and Daniel T. Wise
Journal:
Proc. Amer. Math. Soc. 144 (2016), 1857-1866
MSC (2010):
Primary 20F55
DOI:
https://doi.org/10.1090/proc/13013
Published electronically:
January 26, 2016
MathSciNet review:
3460148
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We use probabilistic methods to prove that many Coxeter groups are incoherent. In particular, this holds for Coxeter groups of uniform exponent 
with sufficiently many generators.
- [BB97] Mladen Bestvina and Noel Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997), no. 3, 445–470. MR 1465330, https://doi.org/10.1007/s002220050168
- [Bie81] Robert Bieri, Homological dimension of discrete groups, 2nd ed., Queen Mary College Mathematical Notes, Queen Mary College, Department of Pure Mathematics, London, 1981. MR 715779
- [Dav08] Michael W. Davis, The geometry and topology of Coxeter groups, London Mathematical Society Monographs Series, vol. 32, Princeton University Press, Princeton, NJ, 2008. MR 2360474
- [GRS80] Ronald L. Graham, Bruce L. Rothschild, and Joel H. Spencer, Ramsey theory, John Wiley & Sons, Inc., New York, 1980. Wiley-Interscience Series in Discrete Mathematics; A Wiley-Interscience Publication. MR 591457
- [HW10] Frédéric Haglund and Daniel T. Wise, Coxeter groups are virtually special, Adv. Math. 224 (2010), no. 5, 1890–1903. MR 2646113, https://doi.org/10.1016/j.aim.2010.01.011
- [MPW13] Eduardo Martínez-Pedroza and Daniel T. Wise, Coherence and negative sectional curvature in complexes of groups, Michigan Math. J. 62 (2013), no. 3, 507–536. MR 3102528, https://doi.org/10.1307/mmj/1378757886
- [MW05] J. P. McCammond and D. T. Wise, Coherence, local quasiconvexity, and the perimeter of 2-complexes, Geom. Funct. Anal. 15 (2005), no. 4, 859–927. MR 2221153, https://doi.org/10.1007/s00039-005-0525-8
- [Sch03] Paul E. Schupp, Coxeter groups, 2-completion, perimeter reduction and subgroup separability, Geom. Dedicata 96 (2003), 179–198. MR 1956839, https://doi.org/10.1023/A:1022155823425
- [Sho91] Hamish Short, Quasiconvexity and a theorem of Howson’s, Group theory from a geometrical viewpoint (Trieste, 1990) World Sci. Publ., River Edge, NJ, 1991, pp. 168–176. MR 1170365
- [Wis04] D. T. Wise, Sectional curvature, compact cores, and local quasiconvexity, Geom. Funct. Anal. 14 (2004), no. 2, 433–468. MR 2062762, https://doi.org/10.1007/s00039-004-0463-x
- [Wis11] Daniel T. Wise, Morse theory, random subgraphs, and incoherent groups, Bull. Lond. Math. Soc. 43 (2011), no. 5, 840–848. MR 2854555, https://doi.org/10.1112/blms/bdr023
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Additional Information
Kasia Jankiewicz
Affiliation:
Department of Mathematics & Statistics, McGill University, Montreal, Quebec, Canada H3A 0B9
Email:
kasia@math.mcgill.ca
Daniel T. Wise
Affiliation:
Department of Mathematics & Statistics, McGill University, Montreal, Quebec, Canada H3A 0B9
Email:
wise@math.mcgill.ca
DOI:
https://doi.org/10.1090/proc/13013
Keywords:
Coxeter groups,
Morse theory,
coherent groups
Received by editor(s):
March 10, 2015
Published electronically:
January 26, 2016
Additional Notes:
This research was supported by NSERC
Communicated by:
Kevin Whyte
Article copyright:
© Copyright 2016
American Mathematical Society
