Detecting free splittings in relatively hyperbolic groups
HTML articles powered by AMS MathViewer
- by François Dahmani and Daniel Groves PDF
- Trans. Amer. Math. Soc. 360 (2008), 6303-6318 Request permission
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
- Mladen Bestvina and Geoffrey Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991), no. 3, 469–481. MR 1096169, DOI 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 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 10.1007/PL00004703
- B. H. Bowditch, Peripheral splittings of groups, Trans. Amer. Math. Soc. 353 (2001), no. 10, 4057–4082. MR 1837220, DOI 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, DOI 10.1007/978-3-662-12494-9
- François Dahmani, Combination of convergence groups, Geom. Topol. 7 (2003), 933–963. MR 2026551, DOI 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 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 10.1016/j.top.2005.03.003
- B. Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998), no. 5, 810–840. MR 1650094, DOI 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- V. Gerasimov, Detecting correctedness of the boundary of a hyperbolic group, unpublished.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 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 10.1090/conm/378/07012
- D. Rebbechi “Algorithmic properties of relatively hyperbolic groups”. Ph.D. thesis (2001).
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. - © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2434288