Paulin, Frédéric Points fixes des automorphismes de groupe hyperbolique. (Fixed points of automorphisms of the hyperbolic group). (French) Zbl 0674.20022 Ann. Inst. Fourier 39, No. 3, 651-662 (1989). 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. Reviewer: F.Paulin Cited in 2 ReviewsCited in 11 Documents MSC: 20F34 Fundamental groups and their automorphisms (group-theoretic aspects) 57M05 Fundamental group, presentations, free differential calculus 20F05 Generators, relations, and presentations of groups 20E36 Automorphisms of infinite groups Keywords:fixed point groups; automorphisms; hyperbolic groups × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] [B1] , Topologie générale, chap. 1 à 4, Hermann, Paris, 1971. · Zbl 0249.54001 [2] [B2] , Topologie générale, chap. 5 à 10, Hermann, Paris, 1971. [3] [C] , Automorphisms of free group have finitely generated fixed point set, J. of Alg., 111, n° 2 (1987), 453-456. · Zbl 0628.20029 [4] [Ge] , Fixed points of automorphisms of free groups, Adv. in Math., 64, n° 1 (1987), 51-85. · Zbl 0616.20014 [5] [GhH] et , Sur les groupes hyperboliques d’après M. Gromov, à paraître, Profess in Math., Birkhaüser. · Zbl 0731.20025 [6] [GoT] and , Automorphisms of free groups and their fixed points, Inv. Math., 78 (1984), 1-12. · Zbl 0548.20016 [7] [Gr1] , 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. · Zbl 0467.53035 [8] [Gr2] , Hyperbolic groups, In : Essays in group theory, Ed. S.M. Gersten, M.S.R.I. Springer-Verlag, 8 (1987), 75-263. · Zbl 0634.20015 [9] [J] , Lectures on three-manifold topology, C.B.M.S. Reg. Conf. Series in Math. A.M.S., 43 (1980). · Zbl 0433.57001 [10] [LyS] and , Combinatorial group theory, a Series of Modern Surveys in Mathematics, Springer-Verlag, 89 (1977). · Zbl 0368.20023 [11] [S] , Graphical theory of automorphisms of free groups, In : Combinatorial group theory and topology, Ann. of Math. Studies, Princeton University Press, 111 (1987). · Zbl 0619.20011 [12] [T] , Hyperbolic structures on 3-manifolds II : surface groups and 3-manifolds which fiber over the circle, à paraître dans Ann. of Math. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.