The rank of actions on R-trees
Gaboriau, Damien ; Levitt, Gilbert
Annales scientifiques de l'École Normale Supérieure, Tome 28 (1995), p. 549-570 / Harvested from Numdam
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@article{ASENS_1995_4_28_5_549_0,
     author = {Gaboriau, Damien and Levitt, Gilbert},
     title = {The rank of actions on $R$-trees},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {28},
     year = {1995},
     pages = {549-570},
     doi = {10.24033/asens.1725},
     mrnumber = {97c:20039},
     zbl = {0835.20038},
     mrnumber = {1341661},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1995_4_28_5_549_0}
}

Gaboriau, Damien; Levitt, Gilbert. The rank of actions on $R$-trees. Annales scientifiques de l'École Normale Supérieure, Tome 28 (1995) pp. 549-570. doi : 10.24033/asens.1725. http://gdmltest.u-ga.fr/item/ASENS_1995_4_28_5_549_0/

[AB] R. Alperin and H. Bass, Length functions of group actions on Λ-trees, in “Combinatorial group theory and topology (S. M. GERSTEN, J. R. STALLINGS, ed.)” (Ann. Math. Studies 111, 1987, Princeton Univ. Press). | MR 89c:20057 | Zbl 0978.20500

[BF1] M. Bestvina and M. Feighn, Bounding the complexity of simplicial group actions on trees (Inv. Math., Vol. 103, 1991, pp. 449-469). | MR 92c:20044 | Zbl 0724.20019

[BF2] M. Bestvina and M. Feighn, Stable actions of groups on real trees, preprint.

[BF3] M. Bestvina and M. Feighn, Outer limits, preprint.

[CL] M. M. Cohen and M. Lustig, Very small group actions on R-trees and Dehn twist automorphisms (Topology (to appear)). | Zbl 0844.20018

[CM] M. Culler and J. W. Morgan, Group actions on R-trees (Proc. Lond. Math. Soc., Vol. 55, 1987, pp. 571-604). | MR 88f:20055 | Zbl 0658.20021

[CV] M. Culler and K. Vogtmann, The boundary of outer space in rank two, in “Arboreal group theory (ALPERIN, ed.)”, MSRI Publ. 19, 1991, pp. 189-230, Springer Verlag. | MR 92i:57001 | Zbl 0786.57002

[Du] M. J. Dunwoody, Groups acting on R-trees (Comm. in Alg., Vol. 19, 1991, pp. 2125-2136). | MR 92i:20028a | Zbl 0767.20011

[FLP] A. Fathi, F. Laudenbach and V. Poenaru, Travaux de Thurston sur les surfaces (Astérisque, Vol. 66-67, 1979, S.M.F., Paris). | MR 82m:57003

[GLP1] D. Gaboriau, G. Levitt and F. Paulin, Pseudogroups of isometries of R and Rips' theorem on free actions on R-trees (Isr. Jour. Math., Vol. 87, 1994, pp. 403-428). | MR 95e:20042 | Zbl 0824.57001

[GLP2] D. Gaboriau, G. Levitt and F. Paulin, Pseudogroups of isometries of R and reconstruction of free actions on R-trees (Erg. Th. Dyn. Syst., Vol. 15, 1995, pp. 1-20). | MR 96i:57011 | Zbl 0839.58022

[GS] H. Gillet and P. B. Shalen, Dendrology of groups in low Q-ranks (Jour. Diff. Geom., Vol. 32, 1990, pp. 605-712). | MR 92b:57003 | Zbl 0732.20011

[GSS] H. Gillet, P. B. Shalen and R. K. Skora, Simplicial approximation and low-rank trees (Comm. Math. Helv., Vol. 66, 1991, pp. 521-540). | MR 93a:20038 | Zbl 0794.20038

[HW] W. Hurewicz and H. Wallman, Dimension Theory, Princeton Univ. Press, 1969.

[Ji] R. Jiang, Branch points and free actions on R-trees, in “Arboreal group theory (ALPERIN, ed.)”, MSRI Publ. 19, 1991, pp. 251-293, Springer Verlag. | MR 92d:57001 | Zbl 0792.57003

[Le1] G. Levitt, La dynamique des pseudogroupes de rotations (Invent. Math., Vol. 113, 1993, pp. 633-670). | MR 94k:58158 | Zbl 0791.58055

[Le2] G. Levitt, Constructing free actions on R-trees (Duke Math. Jour., Vol. 69, 1993, pp. 615-633). | MR 94b:20035 | Zbl 0794.57001

[Le3] G. Levitt, Graphs of actions on R-trees (Comm. Math. Helv., Vol. 69, 1994, pp. 28-38). | MR 95h:20033 | Zbl 0802.05044

[Le4] G. Levitt, R-trees and the Bieri-Neumann-Strebel invariant (Publicacions Matemàtiques, Vol. 38, 1994, pp. 195-202). | MR 95f:20045 | Zbl 0829.20038

[Le5] G. Levitt, On the cost of generating an equivalence relation (Erg. Th. Dyn. Syst. (to appear)). | Zbl 0843.28010

[Lu] M. Lustig, Automorphisms, train track and non-simplicial R-tree actions, preprint.

[MNO] J. C. Mayer, J. Nikiel and L. G. Oversteegen, Universal spaces for R-trees (Trans. A.M.S., Vol. 334, 1992, pp. 411-432). | MR 93a:54034 | Zbl 0787.54036

[Mo] J. W. Morgan, Λ-Trees and their applications (Bull. AMS, Vol. 26, 1992, pp. 87-112). | MR 92e:20017 | Zbl 0767.05054

[Pa] F. Paulin, The Gromov topology on R-trees (Top. Appl., Vol. 32, 1989, pp. 197-221). | MR 90k:57015 | Zbl 0675.20033

[Sh1] P. B. Shalen, Dendrology of groups : an introduction, in “Essays in group theory (S. M. GERSTEN, ed.)”, MSRI Publ. 8, 1987, Springer Verlag. | MR 89d:57012 | Zbl 0649.20033

[Sh2] P. B. Shalen, Dendrology and its applications, in “Group theory from a geometrical viewpoint (E. GHYS, A. HAEFLIGER, A. VERJOVSKY, eds.)”, World Scientific, 1991. | MR 94e:57020 | Zbl 0843.20018

[Sk1] R. K. Skora, Splittings of surfaces (Bull. A.M.S., Vol. 23, 1990, pp. 85-90). | MR 90k:57016 | Zbl 0708.30044

[Sk2] R. Skora, Combination theorems for actions on R-trees, preprint.

[Sk3] R. Skora, personal communication.