Points fixes des automorphismes de groupe hyperbolique
Annales de l'Institut Fourier, Volume 39 (1989) no. 3, p. 651-662

We prove that the fixed points set of an automorphism of a hyperbolic group in M. Gromov sense is finitely generated.

Nous montrons que le sous-groupe des points fixes d’un automorphisme d’un groupe hyperbolique au sens de M. Gromov est de type fini.

@article{AIF_1989__39_3_651_0,
     author = {Paulin, Fr\'ed\'eric},
     title = {Points fixes des automorphismes de groupe hyperbolique},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {39},
     number = {3},
     year = {1989},
     pages = {651-662},
     doi = {10.5802/aif.1181},
     zbl = {0674.20022},
     mrnumber = {91a:20030},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1989__39_3_651_0}
}
Paulin, Frédéric. Points fixes des automorphismes de groupe hyperbolique. Annales de l'Institut Fourier, Volume 39 (1989) no. 3, pp. 651-662. doi : 10.5802/aif.1181. http://www.numdam.org/item/AIF_1989__39_3_651_0/

[B1] N. Bourbaki, Topologie générale, chap. 1 à 4, Hermann, Paris, 1971. | Zbl 0249.54001

[B2] N. Bourbaki, Topologie générale, chap. 5 à 10, Hermann, Paris, 1971.

[C] D. Cooper, Automorphisms of free group have finitely generated fixed point set, J. of Alg., 111, n° 2 (1987), 453-456. | MR 89a:20024 | Zbl 0628.20029

[Ge] S.M. Gersten, Fixed points of automorphisms of free groups, Adv. in Math., 64, n° 1 (1987), 51-85. | MR 88f:20042 | Zbl 0616.20014

[GhH] E. Ghys et P. De La Harpe, Sur les groupes hyperboliques d'après M. Gromov, à paraître, Profess in Math., Birkhaüser. | Zbl 0731.20025

[GoT] R.Z. Goldstein and E.C. Turner, Automorphisms of free groups and their fixed points, Inv. Math., 78 (1984), 1-12. | MR 86h:20031 | Zbl 0548.20016

[Gr1] M. Gromov, Hyperbolic manifolds, groups and actions, Riemann surfaces and related topics, Proc. of the 1978th Stony Brook Conference, Ann. of Math. Studies, 97 (1980), 183-215. | MR 82m:53035 | Zbl 0467.53035

[Gr2] M. Gromov, Hyperbolic groups, In : Essays in group theory, Ed. S.M. Gersten, M.S.R.I. Springer-Verlag, 8 (1987), 75-263. | MR 89e:20070 | Zbl 0634.20015

[J] W. Jaco, Lectures on three-manifold topology, C.B.M.S. Reg. Conf. Series in Math. A.M.S., 43 (1980). | MR 81k:57009 | Zbl 0433.57001

[LyS] R.C. Lyndon and P.E. Schupp, Combinatorial group theory, a Series of Modern Surveys in Mathematics, Springer-Verlag, 89 (1977). | MR 58 #28182 | Zbl 0368.20023

[S] J.R. Stallings, Graphical theory of automorphisms of free groups, In : Combinatorial group theory and topology, Ann. of Math. Studies, Princeton University Press, 111 (1987). | MR 88i:20043 | Zbl 0619.20011

[T] W. Thurston, Hyperbolic structures on 3-manifolds II : surface groups and 3-manifolds which fiber over the circle, à paraître dans Ann. of Math.