Actions de groupes sur les arbres
Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Talk no. 808, 41 p.
@incollection{SB_1995-1996__38__97_0,
     author = {Paulin, Fr\'ed\'eric},
     title = {Actions de groupes sur les arbres},
     booktitle = {S\'eminaire Bourbaki : volume 1995/96, expos\'es 805-819},
     series = {Ast\'erisque},
     note = {talk:808},
     pages = {97--137},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {241},
     year = {1997},
     mrnumber = {1472536},
     zbl = {0984.20015},
     language = {fr},
     url = {http://archive.numdam.org/item/SB_1995-1996__38__97_0/}
}
TY  - CHAP
AU  - Paulin, Frédéric
TI  - Actions de groupes sur les arbres
BT  - Séminaire Bourbaki : volume 1995/96, exposés 805-819
AU  - Collectif
T3  - Astérisque
N1  - talk:808
PY  - 1997
SP  - 97
EP  - 137
IS  - 241
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/SB_1995-1996__38__97_0/
LA  - fr
ID  - SB_1995-1996__38__97_0
ER  - 
%0 Book Section
%A Paulin, Frédéric
%T Actions de groupes sur les arbres
%B Séminaire Bourbaki : volume 1995/96, exposés 805-819
%A Collectif
%S Astérisque
%Z talk:808
%D 1997
%P 97-137
%N 241
%I Société mathématique de France
%U http://archive.numdam.org/item/SB_1995-1996__38__97_0/
%G fr
%F SB_1995-1996__38__97_0
Paulin, Frédéric. Actions de groupes sur les arbres, in Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Talk no. 808, 41 p. http://archive.numdam.org/item/SB_1995-1996__38__97_0/

[1] R. Alperin, H. Bass. Length functions of group actions on A-trees, in "Combinatorial group theory and topology", S. Gersten, J. Stallings eds, Princeton Univ. Press (1987), 265-378. | MR | Zbl

[2] H. Bass. Finitely generated subgroup of GL2, dans "Smith conjecture", J. Morgan, H. Bass, eds. Academic Press (1984), 127-136. | MR | Zbl

[3] H. Bass. Covering theory for graphs of groups, J. Pure Appl. Math. 89 (1993) 3-47. | MR | Zbl

[4] H. Bass, R. Kulkarni. Uniform tree lattices, Jour. Amer. Math. Soc 3 (1990) 843-902. | DOI | MR | Zbl

[5] H. Bass, A. Lubotzky. Rigidity of group actions on locally finite trees, Prépublication, 1994. | MR | Zbl

[6] J.-F. Boutot, H. Carayol. Uniformisation p-adique des courbes de Shimura: les théorèmes de Cerednik et Drinfeld, Astérisque 196-197 (1991). | MR | Zbl

[7] M. Bestvina. Degenerations of the hyperbolic space, Duke Math. J., 56 (1988) 143-161. | DOI | MR | Zbl

[8] M. Bestvina, M. Feighn. Bounding the complexity of simplicial group actions on trees, Inv. Math. 103 (1991) 449-469. | DOI | EuDML | MR | Zbl

[9] M. Bestvina, M. Feighn. Stable actions of groups on real trees, Inv. Math. 121 (1995) 287-321. | DOI | EuDML | MR | Zbl

[10] M. Bestvina, M. Feighn. Outer limits, prépublication (Oct. 1992).

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

[12] B. Bowditch. Discrete parabolic groups, J. Diff. Geom. 38 (1993) 559-583. | DOI | MR | Zbl

[13] B. Bowditch. Cut points and canonical splittings of hyperbolic groups, Prépublication Univ. Southampton (Août 1995). | Zbl

[14] F. Bruhat, J. Tits. Groupes réductifs sur un corps local (données radicielles valuées), Pub. Math. I.H.É.S. 41 (1972) 5-252. | DOI | EuDML | Numdam | MR | Zbl

[15] M. Burger, S. Mozes. CAT(-1) spaces, divergence groups and their commensurators, Jour. Amer. Math. Soc 9 (1996) 57-93. | DOI | MR | Zbl

[16] A. Casson, S. Bleiler. Automorphisms of surfaces after Nielsen and Thurston, Lond. Math. Soc. Stud. Text 9, Camb. Univ. Press (1992). | MR | Zbl

[17] I. M. Chiswell. Non standard analysis and the Morgan-Shalen compactification, Quart. J. Math. Oxford 42 (1991) 257-270. | DOI | MR | Zbl

[18] F. M. Choucroun, Analyse harmonique des groupes d'automorphismes d'arbres de Bruhat-Tits, Mémoire 58 Soc. Math. France (1994). | EuDML | Numdam | MR | Zbl

[19] M. Culler, J. Morgan. Groups actions on R-trees, Proc. Lond. Math. Soc 55 (1987) 571-604. | DOI | MR | Zbl

[20] M. Culler, P. B. Shalen. Varieties of group representations and splittings of 3- manifolds, Ann. of Math. 117 (1983) 109-146. | DOI | MR | Zbl

[21] M. Culler, K. Vogtmann. Moduli of graphs and automorphisms of free groups, Invent. Math. 84 (1986) 91-119. | DOI | EuDML | MR | Zbl

[22] M. Culler, K. Vogtmann. The boundary of Outer Space in rank 2, in "Arboreal group theory", R. Alperin ed., pp 189-230, Pub. M.S.R.I. 19, Springer Verlag 1991. | MR | Zbl

[23] T. Delzant. L'image d'un groupe dans un groupe hyperbolique, Comm. Math. Helv. 70 (1995) 267-284. | DOI | EuDML | MR | Zbl

[24] T. Delzant. Décomposition d'un groupe en produit libre ou somme amalgamée, à paraître dans J. Reine. Ang. Math. | EuDML | MR | Zbl

[25] T. Delzant. Finitely presented subgroups of hyperbolic groups, prépublication Univ. Strasbourg 1995. | Zbl

[26] T. Delzant. Groupes de présentation finie opérant dans un espace hyperbolique, en préparation.

[27] L. Van Den Dries, A. Wilkie. On Gromov's theorem concerning groups of polynomial growth and elementary logic, J. Alg. 89 (1984) 349-374. | DOI | MR | Zbl

[28] M. J. Dunwoody. The accessibility of finitely presented groups, Inv. Math. 81 (1985) 449-457. | DOI | EuDML | MR | Zbl

[29] M. J. Dunwoody. An inaccessible group, in "Geometric group theory" Vol. 1, A. Niblo, M. Roller eds, LMS LNS 182, Cambridge Univ. Press, 1993, 75-78. | DOI | MR | Zbl

[30] M. J. Dunwoody. Groups acting on protrees, prépublication Southampton Univ. (Avr. 1994). | Zbl

[31] M. J. Dunwoody, M. E. Sageev. JSJ-splittings for finitely presented groups over slender groups, prépublication Southampton Univ. (Août 1996). | Zbl

[32] A. Fathi, F. Laudenbach, V. Poenaru. Travaux de Thurston sur les surfaces, Astérisque 66-67, Soc. Math. France 1979. | Numdam | MR | Zbl

[33] A. Figa-Talamanka, C. Nebia. Harmonic analysis and representation theory for groups acting on homogeneous trees, Lond. Math. Soc. Lect. Notes Ser. 162, Cambridge Univ. Press 1991. | MR | Zbl

[34] D. Gaboriau. Générateurs indépendants pour les systèmes d'isométries de dimension un, à paraître aux Ann. Inst. Fourier. | EuDML | Numdam | MR | Zbl

[35] D. Gaboriau, G. Levitt. The rank of actions on R-trees, Ann. Scien. Ec. Norm. Sup. (4) 28 (1995) 549-570. | DOI | EuDML | Numdam | MR | Zbl

[36] D. Gaboriau, G. Levitt, F. Paulin. Pseudogroups of isometries of R and Rips' theorem on free actions on R-trees, Israel J. Math. 87 (1994) 403-428. | DOI | MR | Zbl

[37] D. Gaboriau, G. Levitt, F. Paulin. Pseudogroups of isometries of R and reconstruction of free actions on R-trees, Erg. Theo. Dyn. Sys. 15 (1995) 633-652. | MR | Zbl

[38] E. Gekeler. Drinfeld modular curves, Lect. Notes 1231 Springer Verlag (1986). | MR | Zbl

[39] L. Gerritzen, M. Van Der Put. Schottky groups and Mumford curves, Lect. Notes 817 Springer Verlag (1980). | MR | Zbl

[40] É. Ghys. Les groupes hyperboliques, Séminaire Bourbaki 722, Astérisque 189- 190, Soc. Math. France (1990). | EuDML | Numdam | MR | Zbl

[41] É. Ghys, P. De La Harpe, eds. Sur les groupes hyperboliques d'après Mikhael Gromov, Prog. in Math. 83, Birkhäuser 1990. | DOI | MR | Zbl

[42] H. Gillet, P. Shalen. Dendrology of groups in low Q-ranks, J. Diff. Geom. 32 (1990) 605-712. | DOI | MR | Zbl

[43] O. Goldman, N. Iwahori. The space of p -adic norms, Acta Math. 109 (1963) 137-177. | DOI | MR | Zbl

[44] M. Gromov. Hyperbolic groups, in "Essays in group theory", S. Gersten ed., pp. 75-263, MSRI Pub. 8, Springer Verlag 1987. | MR | Zbl

[45] M. Gromov. Asymptotics invariants of infinite groups, Vol. 2 de "Geometric group theory", A. Niblo, M. Roller eds, LMS LNS 182, Cambridge Univ. Press, 1993. | MR

[46] A. Haefliger. Complexes of groups and orbihedra, in "Group theory from a geometrical viewpoint" (E. Ghys, A. Haefliger, A. Verjovsky eds.), 504-540 World Scientific, 1991. | MR | Zbl

[47] H. Imanishi. On codimension one foliations defined by closed one forms with singularities, J. Math. Kyoto Univ. 19 (1979) 285-291. | DOI | MR | Zbl

[48] N. V. Ivanov. Subgroups of Teichmüller modular groups, Trans. Math. Mono. 115, Amer. Math. Soc. (1992). | MR | Zbl

[49] W. H. Jaco, P. B. Shalen. Seifert fibered spaces in 3-manifolds, Memoirs 220, Amer. Math. Soc. 1979. | MR | Zbl

[50] K. Johannson. Homotopy equivalences of 3-manifolds with boundaries, Lect. Notes in Math. 761, Springer Verlag, 1979. | MR | Zbl

[51] B. Kleiner, B. Leeb. Rigidity of quasi-isometries for symmetric spaces of higher rank, Preprint, Jan. 1995. | MR

[52] J.-L. Koszul. Travaux de J. Stallings sur la décomposition des groupes en produits libres, Sém. Bourbaki 1968/1969 n° 356, Lect. Notes 179, Springer Verlag, 1971. | EuDML | Numdam | MR | Zbl

[53] D. Lacombe. Théorèmes de non-décidabilité, Sém. Bourbaki 1963/64 n° 266, Benjamin, 1966. | EuDML | Numdam | MR | Zbl

[54] G. Levitt. La dynamique des pseudogroupes de rotations, Invent. Math. 113 (1993) 633-670. | DOI | EuDML | MR | Zbl

[55] G. Levitt. Constructing free actions on R-trees, Duke Math. J. 69 (1993) 615-633. | DOI | MR | Zbl

[56] G. Levitt, F. Paulin. Geometric group actions on trees, à paraître dans Amer. Jour. Math. | MR | Zbl

[57] Y. Liu. Density of the commensurability group of uniform tree lattices, J. Alg. 165 (1995) 346-359. | DOI | MR | Zbl

[58] A. Lubotzky. Lattices in rank one Lie groups over local fields, GAFA 1 (1991), 405-431. | EuDML | MR | Zbl

[59] A. Lubotzky, S. Mozes, R. Zimmer. Superrigidity for the commensurability group of tree lattices, Comm. Math. Helv. 69 (1994) 523-548. | DOI | EuDML | MR | Zbl

[60] G. Margulis, G. Soifer. Maximal subgroups of infinite index in finitely generated groups, J. Alg. 69 (1981) 1-23. | DOI | MR | Zbl

[61] G. Martin, On discrete isometry groups of negative curvature, Pac. J. Math. 160 (1993), 109-127. | DOI | MR | Zbl

[62] J. Morgan. A-trees and their applications, Bull. A.M.S. 26 (1992) 87-112. | DOI | MR | Zbl

[63] J. Morgan. Groups actions on trees and the compactification of the space of conjugacy classes of SO(n,1)-representations, Topology 25 (1986) 1-33. | DOI | MR | Zbl

[64] J. Morgan, P. Shalen. Valuations, trees and degeneration of hyperbolic structures I, Ann. Math. 122 (1985) 398-476. | MR | Zbl

[65] J. Morgan, P. Shalen. Valuations, trees and degeneration of hyperbolic structures II, III, Ann. Math. 127 (1988) 403-519. | DOI | MR | Zbl

[66] J. Morgan, P. Shalen. Free actions of surface groups on R-trees, Topology 30 (1991) 143-154. | DOI | MR | Zbl

[67] J.-P. Otal. Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3, Astérisque 235, Soc. Math. France (1996). | MR | Zbl

[68] P. Pansu, Sous-groupes discrets des groupes de Lie :rigidité, arithméticité, Sém. Bourbaki 1993/94 n° 778, Astérisque 227, Soc. Math. France (1995), 69-105. | EuDML | Numdam | MR | Zbl

[69] F. Paulin. Topologie de Gromov équivariante, structures hyperboliques et arbres réels, Invent. Math. 94 (1988), 53-80. | DOI | EuDML | MR | Zbl

[70] F. Paulin. Outer automorphisms of hyperbolic groups and small actions on R- trees, in "Arboreal group theory", R. Alperin ed., pp 331-343, Pub. M.S.R.I. 19, Springer Verlag 1991. | MR | Zbl

[71] F. Paulin. Sur les automorphismes extérieurs des groupes hyperboliques, à paraître, Ann. Scien. Ecol. Norm. Sup. | EuDML | Numdam | MR | Zbl

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

[73] V. Poénaru. Travaux de Thurston sur les difféomorphismes des surfaces et l'espace de Teichmüller, Sém. Bourbaki 1978/79 n° 529, Lect. Notes 770, Springer Verlag, 1980. | EuDML | Numdam | MR | Zbl

[74] H. Poincaré, Oeuvres complètes, tome II, Gauthier-Villars, 1952. | MR | Zbl

[75] M. Raynaud. Construction analytique de courbes en géométrie non archimédienne [d'après David Mumford], Séminaire Bourbaki 427, Lect. Notes 383, Springer Verlag (1994), 171-185. | EuDML | Numdam | MR | Zbl

[76] E. Rips, Z. Sela. Structure and rigidity in hyperbolic groups I, Geom. and Func. Ana. 4 (1994), 337-371. | EuDML | MR | Zbl

[77] E. Rips, Z. Sela. Canonical representatives and equations in hyperbolic groups, Inv. Math. 120 (1995), 489-512. | DOI | EuDML | MR | Zbl

[78] E. Rips, Z. Sela. Cyclic splittings of finitely presented groups and the canonical JSJ decomposition, Prépublication Columbia (Avril 1995). | DOI | MR | Zbl

[79] G. Sabbagh. Caractérisation algébrique des groupes de type fini ayant un problème des mots résoluble, Sém. Bourbaki 1974/75 n° 356, Lect. Notes 179, Springer Verlag, 1971. | Numdam | MR | Zbl

[80] G. P. Scott, C. T. C. Wall. Topological methods in group theory, in "Homological group theory", C.T.C. Wall ed., Lond. Math. Soc. Lect. Notes 36, Cambridge Univ. Press (1979) 137-203. | MR | Zbl

[81] Z. Sela. The isomorphism problem for hyperbolic groups I, Ann. Math. 141 (1995) 217-283. | DOI | MR | Zbl

[82] Z. Sela. Acylindrical accessibility for groups, Prépublication Columbia Univ. (1994). | Zbl

[83] Z. Sela. Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank 1 Lie groups II, à paraître dans GAFA. | Zbl

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

[85] J.-P. Serre. Arbres, amalgames, SL2, Astérisque 46 , Soc. Math. France (1983). | Numdam | MR | Zbl

[86] P. Shalen. Dendrology of groups: an introduction, Essays in group theory (S.M. Gersten ed.), M.S.R.I Pub. 8, Springer Verlag, 1987. | MR | Zbl

[87] P. Shalen. Dendrology and its applications, Group theory from a geometrical viewpoint (E. Ghys, A. Haefliger, A. Verjovsky eds.), World Scientific, 1991. | MR | Zbl

[88] E. H. Spanier. Algebraic topology, Tata McGraw Hill (1966). | MR | Zbl

[89] W. Thurston. On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417-432. | DOI | MR | Zbl

[90] W. Thurston. Hyperbolic structures on 3-manifolds I: Deformation of acylindrical manifolds, Ann. of Math. 124 (1986) 203-246. | DOI | MR | Zbl

[91] J. Tits. A "theorem of Lie-Kolchin" for trees, in "Contributions to Algebra: a collection of papers dedicated to Ellis Kolchin", pp. 377-388, H. Bass et al eds, Academic Press 1977. | MR | Zbl

[92] J. Tits. Immeubles de type affine, dans "Buildings and the geometry of diagrams", Proc. CIME Como 1984, L. Rosati ed., Lect. Notes 1181, Springer Verlag, 1986, 159-190. | MR | Zbl

[93] C. T. C. Wall. Pair of relative cohomological dimension one, J. Pure App. Alg. 1 (1971) 141-154. | DOI | MR | Zbl