Points fixes des automorphismes de groupe hyperbolique

Frédéric Paulin

Annales de l'institut Fourier (1989)

  • Volume: 39, Issue: 3, page 651-662
  • ISSN: 0373-0956

Abstract

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

How to cite

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Paulin, Frédéric. "Points fixes des automorphismes de groupe hyperbolique." Annales de l'institut Fourier 39.3 (1989): 651-662. <http://eudml.org/doc/74845>.

@article{Paulin1989,
abstract = {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.},
author = {Paulin, Frédéric},
journal = {Annales de l'institut Fourier},
keywords = {fixed point groups; automorphisms; hyperbolic groups},
language = {fre},
number = {3},
pages = {651-662},
publisher = {Association des Annales de l'Institut Fourier},
title = {Points fixes des automorphismes de groupe hyperbolique},
url = {http://eudml.org/doc/74845},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Paulin, Frédéric
TI - Points fixes des automorphismes de groupe hyperbolique
JO - Annales de l'institut Fourier
PY - 1989
PB - Association des Annales de l'Institut Fourier
VL - 39
IS - 3
SP - 651
EP - 662
AB - 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.
LA - fre
KW - fixed point groups; automorphisms; hyperbolic groups
UR - http://eudml.org/doc/74845
ER -

References

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  2. [B2] N. BOURBAKI, Topologie générale, chap. 5 à 10, Hermann, Paris, 1971. 
  3. [C] D. COOPER, Automorphisms of free group have finitely generated fixed point set, J. of Alg., 111, n° 2 (1987), 453-456. Zbl0628.20029MR89a:20024
  4. [Ge] S.M. GERSTEN, Fixed points of automorphisms of free groups, Adv. in Math., 64, n° 1 (1987), 51-85. Zbl0616.20014MR88f:20042
  5. [GhH] E. GHYS et P. dE LA HARPE, Sur les groupes hyperboliques d'après M. Gromov, à paraître, Profess in Math., Birkhaüser. Zbl0731.20025
  6. [GoT] R.Z. GOLDSTEIN and E.C. TURNER, Automorphisms of free groups and their fixed points, Inv. Math., 78 (1984), 1-12. Zbl0548.20016MR86h:20031
  7. [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. Zbl0467.53035MR82m:53035
  8. [Gr2] M. GROMOV, Hyperbolic groups, In : Essays in group theory, Ed. S.M. Gersten, M.S.R.I. Springer-Verlag, 8 (1987), 75-263. Zbl0634.20015MR89e:20070
  9. [J] W. JACO, Lectures on three-manifold topology, C.B.M.S. Reg. Conf. Series in Math. A.M.S., 43 (1980). Zbl0433.57001MR81k:57009
  10. [LyS] R.C. LYNDON and P.E. SCHUPP, Combinatorial group theory, a Series of Modern Surveys in Mathematics, Springer-Verlag, 89 (1977). Zbl0368.20023MR58 #28182
  11. [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). Zbl0619.20011MR88i:20043
  12. [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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