Detecting free splittings in relatively hyperbolic groups
Authors:
François Dahmani and Daniel Groves
Journal:
Trans. Amer. Math. Soc. 360 (2008), 6303-6318
MSC (2000):
Primary 20F10; Secondary 20F65
DOI:
https://doi.org/10.1090/S0002-9947-08-04486-3
Published electronically:
July 21, 2008
MathSciNet review:
2434288
Full-text PDF Free Access
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.
- Mladen Bestvina and Geoffrey Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991), no. 3, 469–481. MR 1096169, DOI https://doi.org/10.1090/S0894-0347-1991-1096169-1
- B. H. Bowditch, Connectedness properties of limit sets, Trans. Amer. Math. Soc. 351 (1999), no. 9, 3673–3686. MR 1624089, DOI https://doi.org/10.1090/S0002-9947-99-02388-0
- B. H. Bowditch, Boundaries of geometrically finite groups, Math. Z. 230 (1999), no. 3, 509–527. MR 1680044, DOI https://doi.org/10.1007/PL00004703
- B. H. Bowditch, Peripheral splittings of groups, Trans. Amer. Math. Soc. 353 (2001), no. 10, 4057–4082. MR 1837220, DOI https://doi.org/10.1090/S0002-9947-01-02835-5
- B. Bowditch, “Relatively hyperbolic groups”, preprint.
- Martin R. Bridson and André Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319, Springer-Verlag, Berlin, 1999. MR 1744486
- François Dahmani, Combination of convergence groups, Geom. Topol. 7 (2003), 933–963. MR 2026551, DOI https://doi.org/10.2140/gt.2003.7.933
- F. Dahmani, “Finding relative hyperbolic structure”, preprint.
- F. Dahmani and D. Groves, “The isomorphism problem for toral relatively hyperbolic groups”, preprint. Available at http://arxiv.org/abs/math.GR/0512605.
- M. J. Dunwoody, The accessibility of finitely presented groups, Invent. Math. 81 (1985), no. 3, 449–457. MR 807066, DOI https://doi.org/10.1007/BF01388581
- Cornelia Druţu and Mark Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005), no. 5, 959–1058. With an appendix by Denis Osin and Mark Sapir. MR 2153979, DOI https://doi.org/10.1016/j.top.2005.03.003
- B. Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998), no. 5, 810–840. MR 1650094, DOI https://doi.org/10.1007/s000390050075
- V. Gerasimov, Detecting correctedness of the boundary of a hyperbolic group, unpublished.
- M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829, DOI https://doi.org/10.1007/978-1-4613-9586-7_3
- D. Groves and J.F. Manning, Dehn filling in relatively hyperbolic groups, preprint. Available at arxiv.org/math.GR/0601311.
- Olga Kharlampovich and Alexei G. Myasnikov, Effective JSJ decompositions, Groups, languages, algorithms, Contemp. Math., vol. 378, Amer. Math. Soc., Providence, RI, 2005, pp. 87–212. MR 2159316, DOI https://doi.org/10.1090/conm/378/07012
- D. Rebbechi “Algorithmic properties of relatively hyperbolic groups”. Ph.D. thesis (2001).
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
MR Author ID:
714038
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
MR Author ID:
642547
Email:
groves@caltech.edu, groves@math.uic.edu
Received by editor(s):
October 31, 2006
Published electronically:
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.
Article copyright:
© Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.