Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Detecting free splittings in relatively hyperbolic groups

Author(s): François Dahmani; Daniel Groves
Journal: Trans. Amer. Math. Soc. 360 (2008), 6303-6318.
MSC (2000): Primary 20F10; Secondary 20F65
Posted: July 21, 2008
MathSciNet review: 2434288
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We describe an algorithm which determines whether or not a group which is hyperbolic relative to abelian groups admits a nontrivial splitting over a finite group.


References:

1.
M. Bestvina and G. Mess, ``The boundary of negatively curved groups'', J. Amer. Math. Soc. 4 (1991), 469-481. MR 1096169 (93j:20076)

2.
B. Bowditch, ``Connectedness properties of limit sets'', Trans. Amer. Math. Soc. 351 (1999), no. 9, 3673-3686. MR 1624089 (2000d:20056)

3.
B. Bowditch, ``Boundaries of geometrically finite groups'', Math. Z. 230 (1999), no. 3, 509-527. MR 1680044 (2000b:20049)

4.
B. Bowditch, ``Peripheral splittings of groups'', Trans. Amer. Math. Soc. 353 (2001), 4057-4082. MR 1837220 (2002e:20080)

5.
B. Bowditch, ``Relatively hyperbolic groups'', preprint.

6.
M.R. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Springer-Verlag, Berlin, 1999. MR 1744486 (2000k:53038)

7.
F. Dahmani, ``Combination of convergence groups'' Geom. & Topol. 7 (2003), 933-963. MR 2026551 (2005g:20063)

8.
F. Dahmani, ``Finding relative hyperbolic structure'', preprint.

9.
F. Dahmani and D. Groves, ``The isomorphism problem for toral relatively hyperbolic groups'', preprint. Available at http://arxiv.org/abs/math.GR/0512605.

10.
M. Dunwoody, The accessibility of finitely presented groups, Invent. Math. 81 (1985), 449-457. MR 807066 (87d:20037)

11.
C. Druţu and M. Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005), 959-1058. MR 2153979 (2006d:20078)

12.
B. Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998), 810-840. MR 1650094 (99j:20043)

13.
V. Gerasimov, Detecting correctedness of the boundary of a hyperbolic group, unpublished.

14.
M. Gromov, Hyperbolic groups, in Essays in group theory (S.M. Gersten, ed.), Springer Verlag, MSRI Publ. 8 (1987), 75-263. MR 919829 (89e:20070)

15.
D. Groves and J.F. Manning, Dehn filling in relatively hyperbolic groups, preprint. Available at arxiv.org/math.GR/0601311.

16.
O. Kharlampovich, and A. Miasnikov, Effective JSJ decompositions, in Groups, languages, algorithms, Contemp. Math 378 (2005), 87-212. MR 2159316 (2006m:20045)

17.
D. Rebbechi ``Algorithmic properties of relatively hyperbolic groups''. Ph.D. thesis (2001).

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20F10, 20F65

Retrieve articles in all Journals with MSC (2000): 20F10, 20F65


Additional Information:

François Dahmani
Affiliation: Laboratoire E. Picard, Université Paul Sabatier, F-31062 Toulouse, France
Email: dahmani@picard.ups-tlse.fr

Daniel Groves
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Address at time of publication: Department of Mathematics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607-7045
Email: groves@caltech.edu, groves@math.uic.edu

DOI: 10.1090/S0002-9947-08-04486-3
PII: S 0002-9947(08)04486-3
Received by editor(s): October 31, 2006
Posted: July 21, 2008
Additional Notes: The first author acknowledges support from the ANR grant 06-JCJC-0099-01
The second author’s work was supported in part by NSF Grant DMS-0504251.
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia