Skip to main content
SpringerLink
Log in

Stable actions of groups on real trees

  • Published:
Inventiones mathematicae Aims and scope

Abstract

This paper further develops Rips's work on real trees. We study a class of actions called ‘stable’ which includes actions with trivial arc stabilizers and small actions of hyperbolic groups.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [Bes88] M. Bestvina: Degenerations of the hyperbolic space. Duke Math. J.56, 143–161 (1988)

    Google Scholar 

  • [CM87] M. Culler, J. Morgan: Group actions on ℝ-trees. Proc. London. Math. Soc.55, 571–604 (1987)

    Google Scholar 

  • [CV86] M. Culler, K. Vogtmann: Moduli of graphs and automorphisms of free groups. Invent. Math.84, 91–119 (1986)

    Google Scholar 

  • [Hat88] A. Hatcher: Measured lamination spaces for surfaces, from the topological view-point. Top. and its Appl.30, 63–88 (1988)

    Google Scholar 

  • [Lev93] G. Levitt: Constructing free actions on ℝ-trees. Duke Math. J.69, 615–633 (1993)

    Google Scholar 

  • [Mak83] G.S. Makanin: Equations in a free groups. Math. USSR Izvestiya21, 145–163 (1983)

    Google Scholar 

  • [Mor86] J. Morgan: Group actions on trees and the compactification of the space of classes ofSO(n, 1)-representations. Topology25, 1–33 (1986)

    Google Scholar 

  • [Mor92] J. Morgan: Λ-trees and their applications. Bull. Amer. Math. Soc. (N.S.) (1)26, 87–112 (1992)

    Google Scholar 

  • [MS88] J. Morgan, P. Shalen: Valuations, trees, and degenerations of hyperbolic structures, II. Ann. Math. (2)127, 403–465 (1988)

    Google Scholar 

  • [Pau88] F. Paulin: Topologie de Gromov équivariant, structures hyperboliques et arbres réels. Invent. Math.94, 53–80 (1988)

    Google Scholar 

  • [Pau91] F. Paulin: Outer automorphisms of hyperbolic groups and small actions on ℝ-trees. Arboreal Group Theory (R.C. Alperin, ed.), MSRI Publ., vol. 19, pp. 331–343 Springer-Verlag, 1991

  • [Raz85] A.A. Razborov: On systems of equations in a free group. Math. USSR Izvestiya25, 115–162 (1985)

    Google Scholar 

  • [Ser80] J.P. Serre: Trees. Springer-Verlag, 1980

  • [Sha87] P. Shalen, Dendrology of groups: an introduction. Essays in Group Theory (S.M. Gersten, ed.), MSRI Publ., vol. 8, Springer-Verlag, 1987, pp. 265–319

  • [Sha91] P. Shalen, Dendrology and its applications. Group theory from a geometrical view-point (E. Ghys, A. Haefliger, A. Verjovsky, eds.). World Scientific, 1991

Download references

Author information

Author notes

  1. Mladen Bestvina

    Present address: Department of Mathematics, University of Utah, 84112, Salt Lake City, UT, USA

Authors and Affiliations

  1. Department of Mathematics, UCLA, 90024, Los Angeles, CA, USA

    Mladen Bestvina

  2. Department of Mathematics, Rutgers University, 0710 2, Newark, NJ, USA

    Mark Feighn

Authors
  1. Mladen Bestvina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mark Feighn
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Oblatum II-1993 & 15-II-1995

The first author was supported in part by the Presidential Young Investigator Award and the Alfred P. Sloan Foundation. Both authors were supported in part by the NSF. The second author wishes to thank UCLA for its hospitality while the research leading to this manuscript was conducted.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bestvina, M., Feighn, M. Stable actions of groups on real trees. Invent Math 121, 287–321 (1995). https://doi.org/10.1007/BF01884300

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01884300

Keywords

Search

Navigation