Algebraic & Geometric Topology Volume 19, issue 6 (2019)

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ISSN (electronic): 1472-2739

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Local cut points and splittings of relatively hyperbolic groups

Matthew Haulmark

Algebraic & Geometric Topology 19 (2019) 2795–2836

DOI: 10.2140/agt.2019.19.2795

Bibliography

1	R D Anderson, A characterization of the universal curve and a proof of its homogeneity, Ann. of Math. 67 (1958) 313 MR0096180
2	R D Anderson, One-dimensional continuous curves and a homogeneity theorem, Ann. of Math. 68 (1958) 1 MR0096181
3	H J Baues, A Quintero, Infinite homotopy theory, 6, Kluwer (2001) MR1848146
4	B H Bowditch, Cut points and canonical splittings of hyperbolic groups, Acta Math. 180 (1998) 145 MR1638764
5	B H Bowditch, A topological characterisation of hyperbolic groups, J. Amer. Math. Soc. 11 (1998) 643 MR1602069
6	B H Bowditch, Boundaries of geometrically finite groups, Math. Z. 230 (1999) 509 MR1680044
7	B H Bowditch, Connectedness properties of limit sets, Trans. Amer. Math. Soc. 351 (1999) 3673 MR1624089
8	B H Bowditch, Convergence groups and configuration spaces, from: "Geometric group theory down under" (editors J Cossey, W D Neumann, M Shapiro), de Gruyter (1999) 23 MR1714838
9	B H Bowditch, Treelike structures arising from continua and convergence groups, 662, Amer. Math. Soc. (1999) MR1483830
10	B H Bowditch, Peripheral splittings of groups, Trans. Amer. Math. Soc. 353 (2001) 4057 MR1837220
11	B H Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012) MR2922380
12	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
13	S Claytor, Topological immersion of Peanian continua in a spherical surface, Ann. of Math. 35 (1934) 809 MR1503198
14	F Dahmani, Combination of convergence groups, Geom. Topol. 7 (2003) 933 MR2026551
15	F Dahmani, V Guirardel, P Przytycki, Random groups do not split, Math. Ann. 349 (2011) 657 MR2755002
16	R J Daverman, Decompositions of manifolds, 124, Academic (1986) MR872468
17	H Freudenthal, Über die Enden topologischer Räume und Gruppen, Math. Z. 33 (1931) 692 MR1545233
18	R Geoghegan, Topological methods in group theory, 243, Springer (2008) MR2365352
19	V Gerasimov, Expansive convergence groups are relatively hyperbolic, Geom. Funct. Anal. 19 (2009) 137 MR2507221
20	É Ghys, P de la Harpe, editors, Sur les groupes hyperboliques d’après Mikhael Gromov, 83, Birkhäuser (1990) MR1086648
21	B W Groff, Quasi-isometries, boundaries and JSJ-decompositions of relatively hyperbolic groups, J. Topol. Anal. 5 (2013) 451 MR3152211
22	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
23	D Groves, J F Manning, Dehn filling in relatively hyperbolic groups, Israel J. Math. 168 (2008) 317 MR2448064
24	D Groves, J F Manning, Dehn fillings and elementary splittings, Trans. Amer. Math. Soc. 370 (2018) 3017 MR3766840
25	C R Guilbault, Ends, shapes, and boundaries in manifold topology and geometric group theory, from: "Topology and geometric group theory" (editors M W Davis, J Fowler, J F Lafont, I J Leary), Springer Proc. Math. Stat. 184, Springer (2016) 45 MR3598162
26	C R Guilbault, M A Moran, Proper homotopy types and 𝒵–boundaries of spaces admitting geometric group actions, Expo. Math. 37 (2019) 292 MR4007577
27	D P Guralnik, Ends of cusp-uniform groups of locally connected continua, I, Internat. J. Algebra Comput. 15 (2005) 765 MR2160578
28	M Haulmark, Boundary classification and two-ended splittings of groups with isolated flats, J. Topol. 11 (2018) 645 MR3830879
29	G C Hruska, Relative hyperbolicity and relative quasiconvexity for countable groups, Algebr. Geom. Topol. 10 (2010) 1807 MR2684983
30	G C Hruska, B Kleiner, Hadamard spaces with isolated flats, Geom. Topol. 9 (2005) 1501 MR2175151
31	G C Hruska, K Ruane, Connectedness properties and splittings of groups with isolated flats, preprint (2017) arXiv:1705.00784
32	M Kapovich, B Kleiner, Hyperbolic groups with low-dimensional boundary, Ann. Sci. École Norm. Sup. 33 (2000) 647 MR1834498
33	M Mihalik, S Tschantz, Visual decompositions of Coxeter groups, Groups Geom. Dyn. 3 (2009) 173 MR2466022
34	R Myers, Excellent 1–manifolds in compact 3–manifolds, Topology Appl. 49 (1993) 115 MR1206219
35	D V Osin, Elementary subgroups of relatively hyperbolic groups and bounded generation, Internat. J. Algebra Comput. 16 (2006) 99 MR2217644
36	P Papasoglu, E Swenson, From continua to ℝ–trees, Algebr. Geom. Topol. 6 (2006) 1759 MR2263049
37	P Papasoglu, E Swenson, Boundaries and JSJ decompositions of CAT(0)–groups, Geom. Funct. Anal. 19 (2009) 559 MR2545250
38	P Scott, T Wall, Topological methods in group theory, from: "Homological group theory" (editor C T C Wall), London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press (1979) 137 MR564422
39	J P Serre, Trees, Springer (2003) MR1954121
40	E L Swenson, A cutpoint tree for a continuum, from: "Computational and geometric aspects of modern algebra" (editors M Atkinson, N Gilbert, J Howie, S Linton, E Robertson), London Math. Soc. Lecture Note Ser. 275, Cambridge Univ. Press (2000) 254 MR1776779
41	H C Tran, Relations between various boundaries of relatively hyperbolic groups, Internat. J. Algebra Comput. 23 (2013) 1551 MR3143594
42	P Tukia, Homeomorphic conjugates of Fuchsian groups, J. Reine Angew. Math. 391 (1988) 1 MR961162
43	P Tukia, Convergence groups and Gromov’s metric hyperbolic spaces, New Zealand J. Math. 23 (1994) 157 MR1313451
44	P Tukia, Conical limit points and uniform convergence groups, J. Reine Angew. Math. 501 (1998) 71 MR1637829
45	G T Whyburn, Topological characterization of the Sierpiński curve, Fund. Math. 45 (1958) 320 MR0099638
46	S Willard, General topology, Addison-Wesley (1970) MR0264581
47	A Yaman, A topological characterisation of relatively hyperbolic groups, J. Reine Angew. Math. 566 (2004) 41 MR2039323
48	W y Yang, Peripheral structures of relatively hyperbolic groups, J. Reine Angew. Math. 689 (2014) 101 MR3187929