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The last incoherent Artin group
Author:
Daniel T. Wise
Journal:
Proc. Amer. Math. Soc. 141 (2013), 139-149
MSC (2010):
Primary 20F36, 20E06
Posted:
May 16, 2012
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Additional Information
Abstract: We prove that the Artin group  is not coherent.
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Invent. Math. 129 (1997), no. 3, 445–470. MR 1465330
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Mladen
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type, Geom. Topol. 3 (1999), 269–302
(electronic). MR
1714913 (2000h:20079), http://dx.doi.org/10.2140/gt.1999.3.269
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Bieri, Normal subgroups in duality groups and in groups of
cohomological dimension 2, J. Pure Appl. Algebra 7
(1976), no. 1, 35–51. MR 0390078
(52 #10904)
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Thomas
Brady, Artin groups of finite type with three generators,
Michigan Math. J. 47 (2000), no. 2, 313–324. MR 1793627
(2001j:20056), http://dx.doi.org/10.1307/mmj/1030132536
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Kenneth
S. Brown, Cohomology of groups, Graduate Texts in Mathematics,
vol. 87, Springer-Verlag, New York, 1994. Corrected reprint of the
1982 original. MR 1324339
(96a:20072)
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Pierre
Deligne, Les immeubles des groupes de tresses
généralisés, Invent. Math. 17
(1972), 273–302 (French). MR 0422673
(54 #10659)
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Carl
Droms, Jacques
Lewin, and Herman
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MR
1104843 (92b:20040), http://dx.doi.org/10.1016/0022-4049(91)90072-A
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Craig
C. Squier, On certain 3-generator Artin
groups, Trans. Amer. Math. Soc.
302 (1987), no. 1,
117–124. MR
887500 (88g:20069), http://dx.doi.org/10.1090/S0002-9947-1987-0887500-3
- [BB97]
- Mladen Bestvina and Noel Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997), no. 3, 445-470. MR 1465330 (98i:20039)
- [Bes99]
- Mladen Bestvina, Non-positively curved aspects of Artin groups of finite type, Geom. Topol. 3 (1999), 269-302 (electronic). MR 1714913 (2000h:20079)
- [Bie76]
- Robert Bieri, Normal subgroups in duality groups and in groups of cohomological dimension
 , J. Pure Appl. Algebra 7 (1976), no. 1, 35-51. MR 0390078 (52:10904)
- [Bra00]
- Thomas Brady, Artin groups of finite type with three generators, Michigan Math. J. 47 (2000), no. 2, 313-324. MR 1793627 (2001j:20056)
- [Bro94]
- Kenneth S. Brown, Cohomology of groups, Springer-Verlag, New York, 1994, corrected reprint of the 1982 original. MR 1324339 (96a:20072)
- [Del72]
- Pierre Deligne, Les immeubles des groupes de tresses généralisés, Invent. Math. 17 (1972), 273-302. MR 0422673 (54:10659)
- [DLS91]
- Carl Droms, Jacques Lewin, and Herman Servatius, Tree groups and the
 -string pure braid group, J. Pure Appl. Algebra 70 (1991), no. 3, 251-261. MR 1104843 (92b:20040)
- [Dro87]
- Carl Droms, Graph groups, coherence, and three-manifolds, J. Algebra 106 (1987), no. 2, 484-489. MR 88e:57003
- [Gor04]
- C. McA. Gordon, Artin groups,
 -manifolds and coherence, Bol. Soc. Mat. Mexicana (3) 10 (2004), Special Issue, 193-198. MR 2199348 (2006i:57003)
- [Squ87]
- Craig C. Squier, On certain
 -generator Artin groups, Trans. Amer. Math. Soc. 302 (1987), no. 1, 117-124. MR 887500 (88g:20069)
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Additional Information
Daniel T. Wise
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 2K6
Email:
wise@math.mcgill.ca
DOI:
http://dx.doi.org/10.1090/S0002-9939-2012-11507-2
PII:
S 0002-9939(2012)11507-2
Keywords:
Artin group,
coherence
Received by editor(s):
September 8, 2010
Received by editor(s) in revised form:
June 13, 2011
Posted:
May 16, 2012
Additional Notes:
This research was supported by NSERC
Communicated by:
Alexander N. Dranishnikov
Article copyright:
© Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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