Geodesic
Groups acting on dendrons
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 62-74 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A dendron is a continuum (a non-empty connected compact Hausdorff space) in which every two distinct points have a separation point. We prove that if a group $G$ acts on a dendron $D$ by homeomorphisms, then either $D$ contains a $G$-invariant subset consisting of one or two points, or $G$ contains a free non-commutative subgroup and, furthermore, the action is strongly proximal. 
@article{ZNSL_2013_415_a9,
     author = {A. V. Malyutin},
     title = {Groups acting on dendrons},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {62--74},
     year = {2013},
     volume = {415},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_415_a9/}
}
TY  - JOUR
AU  - A. V. Malyutin
TI  - Groups acting on dendrons
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2013
SP  - 62
EP  - 74
VL  - 415
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2013_415_a9/
LA  - ru
ID  - ZNSL_2013_415_a9
ER  - 
%0 Journal Article
%A A. V. Malyutin
%T Groups acting on dendrons
%J Zapiski Nauchnykh Seminarov POMI
%D 2013
%P 62-74
%V 415
%U http://geodesic.mathdoc.fr/item/ZNSL_2013_415_a9/
%G ru
%F ZNSL_2013_415_a9
A. V. Malyutin. Groups acting on dendrons. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 62-74. http://geodesic.mathdoc.fr/item/ZNSL_2013_415_a9/

[1] S. A. Adeleke, P. M. Neumann, Relations related to betweenness: their structure and automorphisms, Memoirs Amer. Math. Soc., 623, Amer. Math. Soc., Providence, 1998 | MR | Zbl

[2] D. V. Anosov, “O vklade N. N. Bogolyubova v teoriyu dinamicheskikh sistem”, UMN, 49:5(299) (1994), 5–20 | MR | Zbl

[3] J. Auslander, Minimal flows and their extensions, North-Holland Math. Stud., 153, North-Holland, 1988 | MR | Zbl

[4] P. de lya Arp, R. I. Grigorchuk, T. Chekerini-Silberstain, “Amenabelnost i paradoksalnye razbieniya dlya psevdogrupp i diskretnykh metricheskikh prostranstv”, Algebra. Topologiya. Differentsialnye uravneniya i ikh prilozheniya, Sbornik statei. K 90-letiyu so dnya rozhdeniya akademika Lva Semenovicha Pontryagina, Tr. MIAN, 224, Nauka, M., 1999, 68–111 | MR | Zbl

[5] M. M. Bogolyubov, “Pro deyaki ergodichni vlastivosti sutsilnikh grupp pretvoren”, Haykvi zapiski KDU im. T. G. Shevchenko. Fiziko-matem. zbirnik, 4:3 (1939), 45–53

[6] V. V. Benyash-Krivets, Khua Syuin, Gruppy s periodicheskimi poparnymi sootnosheniyami, RIVSh, Minsk, 2010

[7] B. H. Bowditch, Treelike structures arising from continua and convergence groups, Memoirs Amer. Math. Soc., 662, Amer. Math. Soc., Providence, 1999 | MR | Zbl

[8] B. H. Bowditch, J. Crisp, “Archimedean actions on median pretrees”, Math. Proc. Camb. Phil. Soc., 130 (2001), 383–400 | DOI | MR | Zbl

[9] J. J. Charatonik, W. J. Charatonik, “Dendrites”, Aportaciones Mat. Comun., 22 (1998), 227–253 | MR | Zbl

[10] I. M. Chiswell, Introduction to $\Lambda$-trees, World Scientific Publishing Co., 2001 | MR | Zbl

[11] M. Culler, J. Morgan, “Group actions on $\mathbb R$-trees”, Proc. London Math. Soc., 55:3 (1987), 571–604 | DOI | MR | Zbl

[12] T. Giordano, P. de la Harpe, “Moyennabilité des groupes dénombrables et actions sur les espaces de Cantor”, C. R. Acad. Sci. Paris Sér. I Math., 324:11 (1997), 1255–1258 | DOI | MR | Zbl

[13] S. Glasner, “Topological dynamics and group theory”, Trans. Amer. Math. Soc.,, 187 (1974), 327–334 | DOI | MR | Zbl

[14] S. Glasner, “Compressibility properties in topological dynamics”, Am. J. Math., 97 (1975), 148–171 | DOI | MR | Zbl

[15] S. Glasner, Proximal flows, Lect. Notes Math., 517, Springer-Verlag, Berlin–New York, 1976 | MR | Zbl

[16] N. Kopteva, G. Williams, “The Tits alternative for non-spherical Pride groups”, Bull. Lond. Math. Soc., 40:1 (2008), 57–64 | DOI | MR | Zbl

[17] R. C. Lyndon, P. E. Schupp, Combinatorial group theory, Springer-Verlag, Berlin ect., 1977 | MR | Zbl

[18] A. V. Malyutin, Predderevya i topologiya tenei, Preprint No 23, POMI, 2012 | MR | Zbl

[19] A. V. Malyutin, “Klassifikatsiya deistvii grupp na pryamoi i okruzhnosti”, Algebra i analiz, 19:2 (2007), 156–182 | MR | Zbl

[20] G. A. Margulis, “Free subgroups of the homeomorphism group of the circle”, C. R. Acad. Sci. Paris Sér. I Math., 331:9 (2000), 669–674 | DOI | MR | Zbl

[21] J. C. Mayer, J. Nikiel, L. G. Oversteegen, “Universal spaces for $\mathbb R$-trees”, Trans. Amer. Math. Soc., 334 (1992), 411–432 | MR | Zbl

[22] J. van Mill, E. Wattel, “Dendrons”, Topology and order structures, Part 1, Math. Centre Tracts, 142, Math. Centrum, Amsterdam, 1981, 59–81 | MR | Zbl

[23] T. B. Muenzenberger, R. E. Smithson, L. E. Ward (Jr.), “Characterizations of arboroids and dendritic spaces”, Pacific J. Math., 102 (1982), 107–121 | DOI | MR | Zbl

[24] J. von Neumann, “Zur allgemeinen Theorie des Masses”, Fund. Math., 13 (1929), 73–116 | Zbl

[25] A. Yu. Olshanskii, “K voprosu o suschestvovanii invariantnogo srednego na gruppe”, UMN, 35:4(214) (1980), 199–200 | MR | Zbl

[26] A. Yu. Ol'shanskii, M. V. Sapir, “Non-amenable finitely presented torsion-by-cyclic groups”, Publ. Math. Inst. Hautes Études Sci., 96 (2002), 43–169, (2003) | DOI | MR | Zbl

[27] I. Pays, A. Valette, “Sous-groupes libres dans les groupes d'automorphismes d'arbres”, Enseign. Math., 37 (1991), 151–174 | MR | Zbl

[28] J.-P. Serre, Trees, Springer, New York, 1980 | MR | Zbl

[29] E. Shi, S. Wang, L. Zhou, “Minimal group actions on dendrites”, Proc. Amer. Math. Soc., 138:1 (2010), 217–223 | DOI | MR | Zbl

[30] L. E. Ward (Jr.), “On dendritic sets”, Duke Math J., 25 (1958), 505–513 | DOI | MR | Zbl

[31] L. E. Ward (Jr.), “Axioms for cutpoints”, General Topology and Modern Analysis, Proc. Conf. (Univ. California, Riverside, Calif., 1980), Academic Press, New York, 1981, 327–336 | MR