Geodesic
Relative quasiconvexity using fine hyperbolic graphs
Martínez-Pedroza, Eduardo1 ; Wise, Daniel T2
1Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton ON L8S 4K1, Canada
2Department of Mathematics & Statistics, McGill University, Burnside Hall, 805 Sherbrooke Street West, Montreal QC H3A 2K6, Canada
Algebraic and Geometric Topology, Tome 11 (2011) no. 1, pp. 477-501
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We provide a new and elegant approach to relative quasiconvexity for relatively hyperbolic groups in the context of Bowditch’s approach to relative hyperbolicity using cocompact actions on fine hyperbolic graphs. Our approach to quasiconvexity generalizes the other definitions in the literature that apply only for countable relatively hyperbolic groups. We also provide an elementary and self-contained proof that relatively quasiconvex subgroups are relatively hyperbolic.

DOI : 10.2140/agt.2011.11.477
Keywords: hyperbolic group, quasiconvex subgroup, fine graph, relatively hyperbolic group

Martínez-Pedroza, Eduardo  1   ; Wise, Daniel T  2

1 Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton ON L8S 4K1, Canada
2 Department of Mathematics & Statistics, McGill University, Burnside Hall, 805 Sherbrooke Street West, Montreal QC H3A 2K6, Canada 
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Martínez-Pedroza, Eduardo; Wise, Daniel T. Relative quasiconvexity using fine hyperbolic graphs. Algebraic and Geometric Topology, Tome 11 (2011) no. 1, pp. 477-501. doi: 10.2140/agt.2011.11.477

[1] B Bowditch, Relatively hyperbolic groups, Preprint (1999)

[2] M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grund. der Math. Wissenschaften 319, Springer (1999)

[3] F Dahmani, Les groupes relativement hyperboliques et leurs bords, PhD Thesis, Univ. Louis Pasteur (Strasbourg I) (2003); Prépublication de l’Inst. de Recherche Math. Avancée 2003/13 (2003)

[4] B Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998) 810

[5] G C Hruska, Relative hyperbolicity and relative quasiconvexity for countable groups, Algebr. Geom. Topol. 10 (2010) 1807

[6] J F Manning, E Martínez-Pedroza, Separation of relatively quasiconvex subgroups, Pacific J. Math. 244 (2010) 309

[7] E Martínez-Pedroza, Combination of quasiconvex subgroups of relatively hyperbolic groups, Groups Geom. Dyn. 3 (2009) 317

[8] E Martínez-Pedroza, D T Wise, Local quasiconvexity of groups acting on small cancellation complexes, to appear in J. Pure Appl. Algebra

[9] D V Osin, Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, Mem. Amer. Math. Soc. 179 no. 843, Amer. Math. Soc. (2006)

[10] P Tukia, Conical limit points and uniform convergence groups, J. Reine Angew. Math. 501 (1998) 71

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