Sur les automorphismes extérieurs des groupes hyperboliques
Paulin, Frédéric
Annales scientifiques de l'École Normale Supérieure, Tome 30 (1997), p. 147-167 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_1997_4_30_2_147_0,
     author = {Paulin, Fr\'ed\'eric},
     title = {Sur les automorphismes ext\'erieurs des groupes hyperboliques},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {30},
     year = {1997},
     pages = {147-167},
     doi = {10.1016/s0012-9593(97)89917-x},
     mrnumber = {98c:20070},
     zbl = {0877.20014},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_1997_4_30_2_147_0}
}

Paulin, Frédéric. Sur les automorphismes extérieurs des groupes hyperboliques. Annales scientifiques de l'École Normale Supérieure, Tome 30 (1997) pp. 147-167. doi : 10.1016/s0012-9593(97)89917-x. http://gdmltest.u-ga.fr/item/ASENS_1997_4_30_2_147_0/

[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). | MR 89c:20057 | Zbl 0978.20500

[Bau] G. Baumslag, Lecture notes on nilpotent groups, (CBMS Reg. Conf. Ser. Math., vol. 2, Amer. Math. Soc. 1971). | MR 44 #315 | Zbl 0241.20001

[Bes] M. Bestvina, Degenerations of the hyperbolic space, (Duke Math. J., vol. 56, 1988, p. 143-161. | MR 89m:57011 | Zbl 0652.57009

[BF1] M. Bestvina et M. Feighn, Stable actions of groups on real trees, (Inv. Math., vol. 121, 1995, p. 287-321). | MR 96h:20056 | Zbl 0837.20047

[BF2] M. Bestvina et M. Feighn, Outer limits, prépublication, Oct. 1992.

[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.

[BH] M. Bestvina et M. Handel, Train tracks and automorphisms of free groups, (Ann. Math., vol. 135, 1992, p. 1-51). | MR 92m:20017 | Zbl 0757.57004

[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). | MR 85k:20126 | Zbl 0551.57004

[Bou] N. Bourbaki, Topologie générale, chap. 1 à 4, Hermann, Paris, 1971. | Zbl 0249.54001

[Bow] B. Bowditch, Group actions on trees and dendrons, Prépublication Univ. Southampton, Nov. 1995.

[Bra] T. Bradly, The integral cohomology of Out+ (F3), à paraître dans J. Pure App. Alg. | Zbl 0798.20042

[Cha] C. Champetier, Propriétés statistiques des groupes de présentation fini, (Adv. Math., vol. 116, 1995, p. 197-262). | MR 96m:20056 | Zbl 0847.20030

[CL] M. Cohen et M. Lustig, Very small group actions on ℝ-trees and Dehn twist automorphisms, (Topology, vol. 34, 1995, p. 575-617). | MR 96g:20053 | Zbl 0844.20018

[CM] M. Culler et J. Morgan, Groups actions on ℝ-trees, (Proc. Lond. Math. Soc, vol. 55, 1987, p. 571-604). | MR 88f:20055 | Zbl 0658.20021

[CV1] M. Culler et K. Vogtmann, Moduli of graphs and automorphisms of free groups, (Invent. Math., vol. 84, 1986, p. 91-119). | MR 87f:20048 | Zbl 0589.20022

[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). | MR 92i:57001 | Zbl 0786.57002

[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). | MR 86g:20027 | Zbl 0552.20024

[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). | MR 85k:20101 | Zbl 0552.20017

[FLP] A. Fathi, F. Laudenbach et V. Poenaru, Travaux de Thurston sur les surfaces, (Astérisque, vol. 66-67, Soc. Math. France, 1979). | MR 82m:57003

[GH] E. Ghys et P. De La Harpe, Sur les groupes hyperboliques d'après Mikhael Gromov (Prog. in Math., vol. 83, Birkhäuser 1990). | MR 92f:53050 | Zbl 0731.20025

[Ghy] E. Ghys, Les groupes hyperboliques, (Séminaire Bourbaki, vol. 722, Astérisque, Soc. Math. France, 1991). | Numdam

[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). | Numdam | MR 97c:20039 | Zbl 0835.20038

[GLL] D. Gaboriau, G. Levitt et M. Lustig, A dendrological proof of the Scott conjecture for automorphisms of free groups, prépublication Toulouse, Mars 1993.

[Gre] F.P. Greenleaf, Invariant means on topological groups, (Van Nostrand Math. Stud., vol. 16, Van Nostrand 1969). | MR 40 #4776 | Zbl 0174.19001

[Gro1] M. Gromov, Groups of polynomial growth and expanding maps, (Pub. I.H.E.S., vol. 53, 1981, p. 53-78). | Numdam | MR 83b:53041 | Zbl 0474.20018

[Gro2] M. Gromov, Hyperbolic groups, (Essays in group theory, S. Gersten ed., pp. 75-263, MSRI Pub., vol. 8, Springer Verlag 1987). | MR 89e:20070 | Zbl 0634.20015

[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). | MR 95m:20041 | Zbl 0841.20039

[GS] H. Gillet et P. Shalen, Dendrology of groups in low ℚ-ranks, (J. Diff. Geom., vol. 32, 1990, p. 605-712). | MR 92b:57003 | Zbl 0732.20011

[Iva] N. Ivanov, Subgroups of Teichmüller modular groups, (Transl. Math. Mono., vol. 115, Amer. Math. Soc. 1992). | MR 93k:57031 | Zbl 0776.57001

[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). | MR 96e:57006 | Zbl 0829.57006

[Lev] G. Levitt, Feuilletages des surfaces, Thèse d'Etat, Univ. Orsay, 1983.

[Lio] I. Liousse, Feuilletages affines de surfaces et actions affines sur les arbres réels, Thèse, Toulouse (Fév. 1994).

[Lus1] M. Lustig, Habilitationsschrift, Bochum, 1992.

[Lus2] M. Lustig, Automorphisms, train tracks, and non-simplicial ℝ-tree actions, Prépublication Bochum, 1993.

[Mor] J. Morgan, Λ-trees and their applications, (Bull. Amer. Math. Soc., vol. 26, 1992, p. 87-112). | MR 92e:20017 | Zbl 0767.05054

[MS] J. Morgan et P. Shalen, Free actions of surface groups on ℝ-trees, (Topology, vol. 30, 1991, p. 143-154). | MR 92e:20016 | Zbl 0726.57001

[Ols] A. Yu. Ol'Shanskii, Almost every group is hyperbolic, (Int. J. Alg. Comp., vol. 2, 1992, p. 1-17). | MR 93j:20068 | Zbl 0779.20016

[Pau1] F. Paulin, The Gromov topology on ℝ-trees, (Topology and its App., vol. 32, 1989, p. 197-221). | MR 90k:57015 | Zbl 0675.20033

[Pau2] F. Paulin, Topologie de Gromov équivariante, structures hyperboliques et arbres réels, (Invent. Math., vol. 94, 1988, p. 53-80). | MR 90d:57015 | Zbl 0673.57034

[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). | MR 92g:57003 | Zbl 0804.57002

[Pau4] F. Paulin, Points fixes des automorphismes de groupe hyperbolique (Ann. Inst. Fourier, vol. 39, 1989, p. 651-662). | Numdam | MR 91a:20030 | Zbl 0674.20022

[Pau5] F. Paulin, De la géométrie et la dynamique des groupes discrets, (Mémoire d'Habilitation, ENS Lyon, Juin 1995).

[RS1] E. Rips et Z. Sela, Structure and rigidity in hyperbolic groups I, (Geom. and Func. Ana., vol. 4, 1994, p. 337-371). | MR 96c:20067 | Zbl 0818.20042

[RS2] E. Rips et Z. Sela, Cyclic splittings of finitely presented groups and the canonical JSJ decomposition, Prépublication Columbia, Avril 1995.

[Sel1] Z. Sela, Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank 1 Lie groups II, Prépublication Princeton, 1993.

[Sel2] Z. Sela, On the Nielsen-Thurston classification and automorphisms of free groups I, II, à paraître dans Duke Math. J. | Zbl 0858.20019

[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). | MR 89d:57012 | Zbl 0649.20033

[Sha2] P. Shalen, Dendrology and its applications, (Group theory from a geometrical viewpoint (E. GHYS, A. HAEFLIGER et A. VERJOVSKY eds.), World Scientific, 1991). | MR 94e:57020 | Zbl 0843.20018

[Sko1] R. Skora, Splittings of surfaces, (Jour. Amer. Math. Soc., vol. 9, 1996, p. 605-616). | MR 96h:57011 | Zbl 0877.57002

[Sko2] R. Skora, Deformations of length functions, prépublication, 1989.

[Thu] W. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, (Bull. Amer. Math. Soc., vol. 19, 1988, p. 417-432). | MR 89k:57023 | Zbl 0674.57008

[Vog] K. Vogtmann, End invariants of the group of outer automorphisms of a free group, (Topology, vol. 34, 1995, p. 533-545). | MR 96h:20068 | Zbl 0833.20044