COMPLEX OF RELATIVELY HYPERBOLIC GROUPS
Glasgow mathematical journal, Tome 61 (2019) no. 3, pp. 657-672

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we prove a combination theorem for a complex of relatively hyperbolic groups. It is a generalization of Martin’s (Geom. Topology18 (2014), 31–102) work for combination of hyperbolic groups over a finite MK-simplicial complex, where k ≤ 0.
PAL, ABHIJIT; PAUL, SUMAN. COMPLEX OF RELATIVELY HYPERBOLIC GROUPS. Glasgow mathematical journal, Tome 61 (2019) no. 3, pp. 657-672. doi: 10.1017/S0017089518000423
@article{10_1017_S0017089518000423,
     author = {PAL, ABHIJIT and PAUL, SUMAN},
     title = {COMPLEX {OF} {RELATIVELY} {HYPERBOLIC} {GROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {657--672},
     year = {2019},
     volume = {61},
     number = {3},
     doi = {10.1017/S0017089518000423},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000423/}
}
TY  - JOUR
AU  - PAL, ABHIJIT
AU  - PAUL, SUMAN
TI  - COMPLEX OF RELATIVELY HYPERBOLIC GROUPS
JO  - Glasgow mathematical journal
PY  - 2019
SP  - 657
EP  - 672
VL  - 61
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000423/
DO  - 10.1017/S0017089518000423
ID  - 10_1017_S0017089518000423
ER  - 
%0 Journal Article
%A PAL, ABHIJIT
%A PAUL, SUMAN
%T COMPLEX OF RELATIVELY HYPERBOLIC GROUPS
%J Glasgow mathematical journal
%D 2019
%P 657-672
%V 61
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000423/
%R 10.1017/S0017089518000423
%F 10_1017_S0017089518000423

[1] Bestvina, M. and Feighn, M., A combination theorem for negatively curved groups, J. Differ. Geom. 35 (1992), 85–101. Google Scholar | DOI

[2] Bowditch, B. H., A topological characterization of hyperbolic groups, J. Amer. Math. Soc. 11 (1998), 643–667. Google Scholar | DOI

[3] Bowditch, B. H., Relatively hyperbolic groups, Int. J. Algebra Comput. 22 (2012), 1250016, 66pp. Google Scholar | DOI

[4] Bridson, M. R. and Haefliger, A., Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol 319 (Springer-Verlag, Berlin, 1999). Google Scholar | DOI

[5] Dahmani, F., Combination of convergence groups, Geom. Topol. (2003), 933–963. Google Scholar | DOI

[6] Farb, B., Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998), 810–840. Google Scholar | DOI

[7] Martin, A., Non-positively curved complexes of groups and boundaries, Geom. Topol. 18 (2014), 31–102. Google Scholar | DOI

[8] Gitik, R., Mitra, M., E. Rips and M. Sageev, Width of subgroups, Trans. AMS 350 (1) (1998), 321–329. Google Scholar | DOI

[9] Gromov, M., Essays in group theory, (ed Gersten) MSRI Publ., vol. 8 (Springer Verlag, 1985), 75–263. Google Scholar

[10] Groves, D. and Manning, J. F., Dehn filling in relatively hyperbolic groups, Isr. J. Math. 168 (2008), 317–429. Google Scholar | DOI

[11] Hruska, G. Christopher and Wise, D. T., Packing subgroups in relatively hyperbolic groups, Geom. Topol. 13 (2009), 1945–1988. Google Scholar | DOI

[12] Haefliger, A., Complexes of groups and orbihedra, in Proceedings of the Group Theory from a Geometrical Viewpoint ICTP, Trieste, Italy, 26 March–6 April 1990. Google Scholar

[13] Christopher, G. Hruska, Relative hyperbolicity and relative quasiconvexity for countable groups, Algebr. Geom. Topol. 10 (2010), 1807–1856. Google Scholar

[14] Kapovich, I., The combination theorem and quasiconvexity, Int. J. Algebra Comput. 11 (2001), 185. Google Scholar | DOI

[15] Minasyan, A. and Osin, D., Acylindrical hyperbolicity of group acting on trees, Math. Ann. 362 (2015), 1055–1105. Google Scholar | DOI

[16] Mitra, M., Cannon-Thurston maps for trees of hyperbolic metric spaces, J. Differ. Geom. 48 (1) (1998), 135–164. Google Scholar | DOI

[17] Mitra, M., Height in splitting of hyperbolic groups, Proc. Indian Acad. Sci. (Math. Sci.) 114 (1) (2004), 39–54. Google Scholar | DOI

[18] Mj, M. and Reeves, L., A combination theorem for strong relative hyperbolicity, Geom. Topol. 12 (2008), 1777–1798. Google Scholar | DOI

[19] Mj, M. and Pal, A., Relative hyperbolicity, trees of spaces and Cannon-Thurston maps, Geom. Dedicata 151 (1) (2011), 59–75. Google Scholar | DOI

[20] Mj, M. and Sardar, P., Combination theorem for metric bundles, Geom. Funct. Anal. 22 (6) (2012), 1636–1707. Google Scholar | DOI

[21] Serre, J.-P., Arbres, amalgames, SL2. RŤÒdigŤÒ avec la collaboration de Hyman Bass Asterisque, No. 46 (Societe Mathematique de France, Paris, 1977). Google Scholar

[22] Serre, J.-P., Trees (Translated from the French by John Stillwell) (Springer-Verlag, Berlin Heidelberg, 1980). ISBN 3-540-10103-9. Google Scholar

[23] Szczepanski, A., Relatively hyperbolic groups, Michigan Math. J. 45 (3) (1998), 611–618. Google Scholar

[24] Tukia, P., Generalizations of Fuchsian and Kleinian groups, First European Congress of Mathematics, Vol. II (Paris, 1992) 447–461. Google Scholar

[25] Yang, W.-Y., Limit sets of relatively hyperbolic groups, Geometriae Dedicata 156 (1) (2012), 1–12. Google Scholar | DOI

[26] Yaman, A., A topological characterisation of relatively hyperbolic groups, 2004(566) (2004), 41–89. Google Scholar | DOI

Cité par Sources :