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Transactions of the American Mathematical Society

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On suspensions and conjugacy of hyperbolic automorphisms

Author: François Dahmani
Journal: Trans. Amer. Math. Soc. 368 (2016), 5565-5577
MSC (2010): Primary 20F10, 20F28, 20F67
Published electronically: October 20, 2015
MathSciNet review: 3458391
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Abstract: We remark that the conjugacy problem for pairs of hyperbolic automorphisms of a finitely presented group (typically a free group) is decidable. The solution that we propose uses the isomorphism problem for the suspensions, and the study of their automorphism group.

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  • [ALM] Goulnara Arzhantseva, Jean-François Lafont, and Ashot Minasyan, Isomorphism versus commensurability for a class of finitely presented groups, J. Group Theory 17 (2014), no. 2, 361-378. MR 3176665,
  • [BMV] O. Bogopolski, A. Martino, and E. Ventura, Orbit decidability and the conjugacy problem for some extensions of groups, Trans. Amer. Math. Soc. 362 (2010), no. 4, 2003-2036. MR 2574885 (2011e:20045),
  • [Ba] Hyman Bass, Covering theory for graphs of groups, J. Pure Appl. Algebra 89 (1993), no. 1-2, 3-47. MR 1239551 (94j:20028),
  • [Br1] P. Brinkmann, Hyperbolic automorphisms of free groups, Geom. Funct. Anal. 10 (2000), no. 5, 1071-1089. MR 1800064 (2001m:20061),
  • [Br2] Peter Brinkmann, Splittings of mapping tori of free group automorphisms, Geom. Dedicata 93 (2002), 191-203. MR 1934698 (2003j:20038),
  • [D] François Dahmani, Existential questions in (relatively) hyperbolic groups, Israel J. Math. 173 (2009), 91-124. MR 2570661 (2011a:20110),
  • [DGu1] François Dahmani and Vincent Guirardel, Foliations for solving equations in groups: free, virtually free, and hyperbolic groups, J. Topol. 3 (2010), no. 2, 343-404. MR 2651364 (2012a:20069),
  • [DGu2] François Dahmani and Vincent Guirardel, The isomorphism problem for all hyperbolic groups, Geom. Funct. Anal. 21 (2011), no. 2, 223-300. MR 2795509 (2012e:20097),
  • [DGr] François Dahmani and Daniel Groves, The isomorphism problem for toral relatively hyperbolic groups, Publ. Math. Inst. Hautes Études Sci. 107 (2008), 211-290. MR 2434694 (2009i:20081),
  • [Lo] Jérôme E. Los, On the conjugacy problem for automorphisms of free groups, Topology 35 (1996), no. 3, 779-808. With an addendum by the author. MR 1396778 (97h:20031),
  • [Lu1] M. Lustig, Structure and conjugacy for automorphisms of free groups I, MPI-Bonn preprint series 2000, No. 241;
  • [Lu2] M. Lustig, Structure and conjugacy for automorphisms of free groups II, MPI-Bonn preprint series 2001, No. 4;
  • [Lu3] M. Lustig, Conjugacy and centralizers for iwip automorphisms of free groups, Geometric group theory, Trends Math., Birkhäuser, Basel, 2007, pp. 197-224. MR 2395795 (2009c:20063),
  • [P] P. Papasoglu, An algorithm detecting hyperbolicity, Geometric and computational perspectives on infinite groups (Minneapolis, MN and New Brunswick, NJ, 1994) DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 25, Amer. Math. Soc., Providence, RI, 1996, pp. 193-200. MR 1364185 (96k:20075)
  • [Sel] Z. Sela, The isomorphism problem for hyperbolic groups. I, Ann. of Math. (2) 141 (1995), no. 2, 217-283. MR 1324134 (96b:20049),
  • [Ser] Jean-Pierre Serre, Arbres, amalgames, $ {\rm SL}_{2}$, Société Mathématique de France, Paris, 1977 (French). Avec un sommaire anglais; Rédigé avec la collaboration de Hyman Bass; Astérisque, No. 46. MR 0476875 (57 #16426)
  • [Sta] John Stallings, Group theory and three-dimensional manifolds, Yale University Press, New Haven, Conn.-London, 1971. A James K. Whittemore Lecture in Mathematics given at Yale University, 1969; Yale Mathematical Monographs, 4. MR 0415622 (54 #3705)

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Additional Information

François Dahmani
Affiliation: Institut Fourier UMR5582, Université Grenoble Alpes, F-38402 Grenoble, France

Received by editor(s): April 8, 2014
Received by editor(s) in revised form: July 11, 2014
Published electronically: October 20, 2015
Additional Notes: The author was partially supported by the ANR (grant 2011-BS01-013-02, and LabEx Persyval 11-LABX-0025) and the Institut Universitaire de France
Article copyright: © Copyright 2015 American Mathematical Society

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