Sur les automorphismes extérieurs des groupes hyperboliques

Frédéric Paulin

Annales scientifiques de l'École Normale Supérieure (1997)

  • Volume: 30, Issue: 2, page 147-167
  • ISSN: 0012-9593

How to cite

top

Paulin, Frédéric. "Sur les automorphismes extérieurs des groupes hyperboliques." Annales scientifiques de l'École Normale Supérieure 30.2 (1997): 147-167. <http://eudml.org/doc/82428>.

@article{Paulin1997,
author = {Paulin, Frédéric},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {groups of outer automorphisms; word-hyperbolic groups; actions on trees; free groups; Culler-Vogtmann outer spaces; fixed points subgroups; finitely presented groups},
language = {fre},
number = {2},
pages = {147-167},
publisher = {Elsevier},
title = {Sur les automorphismes extérieurs des groupes hyperboliques},
url = {http://eudml.org/doc/82428},
volume = {30},
year = {1997},
}

TY - JOUR
AU - Paulin, Frédéric
TI - Sur les automorphismes extérieurs des groupes hyperboliques
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1997
PB - Elsevier
VL - 30
IS - 2
SP - 147
EP - 167
LA - fre
KW - groups of outer automorphisms; word-hyperbolic groups; actions on trees; free groups; Culler-Vogtmann outer spaces; fixed points subgroups; finitely presented groups
UR - http://eudml.org/doc/82428
ER -

References

top
  1. [AB] R. ALPERIN et H. BASS, Length functions of group actions on Λ-trees, (Combinatorial group theory and topology, S. Gersten, J. Stallings eds, Princeton Univ. Press 1987, p. 265-378). Zbl0978.20500MR89c:20057
  2. [Bau] G. BAUMSLAG, Lecture notes on nilpotent groups, (CBMS Reg. Conf. Ser. Math., vol. 2, Amer. Math. Soc. 1971). Zbl0241.20001MR44 #315
  3. [Bes] M. BESTVINA, Degenerations of the hyperbolic space, (Duke Math. J., vol. 56, 1988, p. 143-161. Zbl0652.57009MR89m:57011
  4. [BF1] M. BESTVINA et M. FEIGHN, Stable actions of groups on real trees, (Inv. Math., vol. 121, 1995, p. 287-321). Zbl0837.20047MR96h:20056
  5. [BF2] M. BESTVINA et M. FEIGHN, Outer limits, prépublication, Oct. 1992. 
  6. [BFH] M. BESTVINA, M. FEIGHN et M. HANDEL, The Tits alternative for Out(Fn) I : Dynamics of exponentially growing automorphisms, II : A Kolchin type theorem, III : Solvable subgroups, Prépublications Univ. Utah, 1996. 
  7. [BH] M. BESTVINA et M. HANDEL, Train tracks and automorphisms of free groups, (Ann. Math., vol. 135, 1992, p. 1-51). Zbl0757.57004MR92m:20017
  8. [BLM] J. BIRMAN, A. LUBOTZKY et J. MCCARTHY, Abelian and solvable subgroups of the mapping class group, (Duke Math. J., vol. 50, 1983, p. 1107-1120). Zbl0551.57004MR85k:20126
  9. [Bou] N. BOURBAKI, Topologie générale, chap. 1 à 4, Hermann, Paris, 1971. Zbl0249.54001
  10. [Bow] B. BOWDITCH, Group actions on trees and dendrons, Prépublication Univ. Southampton, Nov. 1995. 
  11. [Bra] T. BRADLY, The integral cohomology of Out+ (F3), à paraître dans J. Pure App. Alg. Zbl0798.20042
  12. [Cha] C. CHAMPETIER, Propriétés statistiques des groupes de présentation fini, (Adv. Math., vol. 116, 1995, p. 197-262). Zbl0847.20030MR96m:20056
  13. [CL] M. COHEN et M. LUSTIG, Very small group actions on ℝ-trees and Dehn twist automorphisms, (Topology, vol. 34, 1995, p. 575-617). Zbl0844.20018MR96g:20053
  14. [CM] M. CULLER et J. MORGAN, Groups actions on ℝ-trees, (Proc. Lond. Math. Soc, vol. 55, 1987, p. 571-604). Zbl0658.20021MR88f:20055
  15. [CV1] M. CULLER et K. VOGTMANN, Moduli of graphs and automorphisms of free groups, (Invent. Math., vol. 84, 1986, p. 91-119). Zbl0589.20022MR87f:20048
  16. [CV2] M. CULLER et K. VOGTMANN, The boundary of Outer Space in rank 2, (Arboreal group theory, R. Alperin ed., pp 189-230, Pub. M.S.R.I. Vol. 19, Springer Verlag 1991). Zbl0786.57002MR92i:57001
  17. [Cul] M. CULLER, Finite groups of outer automorphisms of a free group, (Contributions to group theory, K. Appel, J. Ratcliffe, P. Schupp, eds, pp 197-207, Contemp. Math. Amer. Math. Soc). Zbl0552.20024MR86g:20027
  18. [DW] L. VAN DEN DRIES et A. WILKIE, On Gromov's theorem concerning groups of polynomial growth and elementary logic, (J. Alg., vol. 89, 1984, p. 349-374). Zbl0552.20017MR85k:20101
  19. [FLP] A. FATHI, F. LAUDENBACH et V. POENARU, Travaux de Thurston sur les surfaces, (Astérisque, vol. 66-67, Soc. Math. France, 1979). MR82m:57003
  20. [GH] E. GHYS et P. DE LA HARPE, Sur les groupes hyperboliques d'après Mikhael Gromov (Prog. in Math., vol. 83, Birkhäuser 1990). Zbl0731.20025MR92f:53050
  21. [Ghy] E. GHYS, Les groupes hyperboliques, (Séminaire Bourbaki, vol. 722, Astérisque, Soc. Math. France, 1991). 
  22. [GL] D. GABORIAU et G. LEVITT, The rank of actions on ℝ-trees, (Ann. Scien. Ec. Norm. Sup. (4), vol. 28, 1995, p. 549-570). Zbl0835.20038MR97c:20039
  23. [GLL] D. GABORIAU, G. LEVITT et M. LUSTIG, A dendrological proof of the Scott conjecture for automorphisms of free groups, prépublication Toulouse, Mars 1993. Zbl0904.20014
  24. [Gre] F.P. GREENLEAF, Invariant means on topological groups, (Van Nostrand Math. Stud., vol. 16, Van Nostrand 1969). Zbl0174.19001MR40 #4776
  25. [Gro1] M. GROMOV, Groups of polynomial growth and expanding maps, (Pub. I.H.E.S., vol. 53, 1981, p. 53-78). Zbl0474.20018MR83b:53041
  26. [Gro2] M. GROMOV, Hyperbolic groups, (Essays in group theory, S. Gersten ed., pp. 75-263, MSRI Pub., vol. 8, Springer Verlag 1987). Zbl0634.20015MR89e:20070
  27. [Gro3] M. GROMOV, Asymptotics invariants of infinite groups, (Vol. 2 de Geometric group theory, A. Niblo, M. Roller eds, LMS LNS, vol. 182, Cambridge Univ. Press, 1993). Zbl0841.20039MR95m:20041
  28. [GS] H. GILLET et P. SHALEN, Dendrology of groups in low ℚ-ranks, (J. Diff. Geom., vol. 32, 1990, p. 605-712). Zbl0732.20011MR92b:57003
  29. [Iva] N. IVANOV, Subgroups of Teichmüller modular groups, (Transl. Math. Mono., vol. 115, Amer. Math. Soc. 1992). Zbl0776.57001MR93k:57031
  30. [KL] M. KAPOVICH et B. LEEB, On asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds, (GAFA, vol. 5, 1995, p. 582-603). Zbl0829.57006MR96e:57006
  31. [Lev] G. LEVITT, Feuilletages des surfaces, Thèse d'Etat, Univ. Orsay, 1983. 
  32. [Lio] I. LIOUSSE, Feuilletages affines de surfaces et actions affines sur les arbres réels, Thèse, Toulouse (Fév. 1994). 
  33. [Lus1] M. LUSTIG, Habilitationsschrift, Bochum, 1992. 
  34. [Lus2] M. LUSTIG, Automorphisms, train tracks, and non-simplicial ℝ-tree actions, Prépublication Bochum, 1993. 
  35. [Mor] J. MORGAN, Λ-trees and their applications, (Bull. Amer. Math. Soc., vol. 26, 1992, p. 87-112). Zbl0767.05054MR92e:20017
  36. [MS] J. MORGAN et P. SHALEN, Free actions of surface groups on ℝ-trees, (Topology, vol. 30, 1991, p. 143-154). Zbl0726.57001MR92e:20016
  37. [Ols] A. Yu. OL'SHANSKII, Almost every group is hyperbolic, (Int. J. Alg. Comp., vol. 2, 1992, p. 1-17). Zbl0779.20016MR93j:20068
  38. [Pau1] F. PAULIN, The Gromov topology on ℝ-trees, (Topology and its App., vol. 32, 1989, p. 197-221). Zbl0675.20033MR90k:57015
  39. [Pau2] F. PAULIN, Topologie de Gromov équivariante, structures hyperboliques et arbres réels, (Invent. Math., vol. 94, 1988, p. 53-80). Zbl0673.57034MR90d:57015
  40. [Pau3] F. PAULIN, Outer automorphisms of hyperbolic groups and small actions on ℝ-trees, (Arboreal group theory, R. Alperin ed., pp 331-343, Pub. M.S.R.I., vol. 19, Springer Verlag, 1991). Zbl0804.57002MR92g:57003
  41. [Pau4] F. PAULIN, Points fixes des automorphismes de groupe hyperbolique (Ann. Inst. Fourier, vol. 39, 1989, p. 651-662). Zbl0674.20022MR91a:20030
  42. [Pau5] F. PAULIN, De la géométrie et la dynamique des groupes discrets, (Mémoire d'Habilitation, ENS Lyon, Juin 1995). 
  43. [RS1] E. RIPS et Z. SELA, Structure and rigidity in hyperbolic groups I, (Geom. and Func. Ana., vol. 4, 1994, p. 337-371). Zbl0818.20042MR96c:20067
  44. [RS2] E. RIPS et Z. SELA, Cyclic splittings of finitely presented groups and the canonical JSJ decomposition, Prépublication Columbia, Avril 1995. 
  45. [Sel1] Z. SELA, Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank 1 Lie groups II, Prépublication Princeton, 1993. 
  46. [Sel2] Z. SELA, On the Nielsen-Thurston classification and automorphisms of free groups I, II, à paraître dans Duke Math. J. Zbl0858.20019
  47. [Sha1] P. SHALEN, Dendrology of groups : an introduction, (Essays in group theory (S.M. Gersten ed.), M.S.R.I Pub., vol. 8, Springer Verlag, 1987). Zbl0649.20033MR89d:57012
  48. [Sha2] P. SHALEN, Dendrology and its applications, (Group theory from a geometrical viewpoint (E. GHYS, A. HAEFLIGER et A. VERJOVSKY eds.), World Scientific, 1991). Zbl0843.20018MR94e:57020
  49. [Sko1] R. SKORA, Splittings of surfaces, (Jour. Amer. Math. Soc., vol. 9, 1996, p. 605-616). Zbl0877.57002MR96h:57011
  50. [Sko2] R. SKORA, Deformations of length functions, prépublication, 1989. 
  51. [Thu] W. THURSTON, On the geometry and dynamics of diffeomorphisms of surfaces, (Bull. Amer. Math. Soc., vol. 19, 1988, p. 417-432). Zbl0674.57008MR89k:57023
  52. [Vog] K. VOGTMANN, End invariants of the group of outer automorphisms of a free group, (Topology, vol. 34, 1995, p. 533-545). Zbl0833.20044MR96h:20068

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.