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

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.

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

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     title = {Points fixes des automorphismes de groupe hyperbolique},
     journal = {Annales de l'Institut Fourier},
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     publisher = {Institut Fourier},
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Paulin, Frédéric. Points fixes des automorphismes de groupe hyperbolique. Annales de l'Institut Fourier, Tome 39 (1989) no. 3, pp. 651-662. doi : 10.5802/aif.1181. http://archive.numdam.org/articles/10.5802/aif.1181/

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

[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 | Zbl

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

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

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

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

[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.

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