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Quasiconvexity of virtual joins and separability of products in relatively hyperbolic groups

Ashot Minasyan and Lawk Mineh

Algebraic & Geometric Topology 25 (2025) 399–488
Bibliography
1 I Agol, Tameness of hyperbolic 3-manifolds, preprint (2004) arXiv:math/0405568
2 I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553
3 E Alibegović, A combination theorem for relatively hyperbolic groups, Bull. London Math. Soc. 37 (2005) 459 MR2131400
4 R B J T Allenby, R J Gregorac, On locally extended residually finite groups, from: "Conference on group theory" (editors R W Gatterdam, K W Weston), Lecture Notes in Math. 319, Springer (1973) 9 MR382450
5 M Baker, D Cooper, A combination theorem for convex hyperbolic manifolds, with applications to surfaces in 3-manifolds, J. Topol. 1 (2008) 603 MR2417445
6 H Bigdely, D T Wise, Quasiconvexity and relatively hyperbolic groups that split, Michigan Math. J. 62 (2013) 387 MR3079269
7 B H Bowditch, Geometrical finiteness for hyperbolic groups, J. Funct. Anal. 113 (1993) 245 MR1218098
8 B H Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012) 1250016 MR2922380
9 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
10 R Brooks, Circle packings and co-compact extensions of Kleinian groups, Invent. Math. 86 (1986) 461 MR860677
11 D Calegari, D Gabai, Shrinkwrapping and the taming of hyperbolic 3-manifolds, J. Amer. Math. Soc. 19 (2006) 385 MR2188131
12 R D Canary, A covering theorem for hyperbolic 3-manifolds and its applications, Topology 35 (1996) 751 MR1396777
13 T Coulbois, Propriétés de Ribes–Zalesskii, topologie profinie, produit libre et généralisations, PhD thesis, Université Paris VII (2000)
14 T Coulbois, Free product, profinite topology and finitely generated subgroups, Internat. J. Algebra Comput. 11 (2001) 171 MR1829049
15 F Dahmani, Combination of convergence groups, Geom. Topol. 7 (2003) 933 MR2026551
16 W Dicks, M J Dunwoody, Groups acting on graphs, 17, Cambridge Univ. Press (1989) MR1001965
17 C Druţu, M Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
18 E Einstein, D Groves, Relatively geometric actions on CAT(0) cube complexes, J. Lond. Math. Soc. 105 (2022) 691 MR4411337
19 E Einstein, T Ng, Relative cubulation of small cancellation free products, preprint (2021) arXiv:2111.03008
20 B Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998) 810 MR1650094
21 R Gitik, Graphs and separability properties of groups, J. Algebra 188 (1997) 125 MR1432351
22 R Gitik, On the profinite topology on negatively curved groups, J. Algebra 219 (1999) 80 MR1707664
23 R Gitik, Ping-pong on negatively curved groups, J. Algebra 217 (1999) 65 MR1700476
24 R Gitik, E Rips, On separability properties of groups, Internat. J. Algebra Comput. 5 (1995) 703 MR1365198
25 M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
26 D Groves, J F Manning, Dehn filling in relatively hyperbolic groups, Israel J. Math. 168 (2008) 317 MR2448064
27 D Groves, J F Manning, Specializing cubulated relatively hyperbolic groups, J. Topol. 15 (2022) 398 MR4413505
28 F Haglund, D T Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008) 1551 MR2377497
29 E Hamilton, H Wilton, P A Zalesskii, Separability of double cosets and conjugacy classes in 3-manifold groups, J. Lond. Math. Soc. 87 (2013) 269 MR3022716
30 G C Hruska, Relative hyperbolicity and relative quasiconvexity for countable groups, Algebr. Geom. Topol. 10 (2010) 1807 MR2684983
31 T Hsu, D T Wise, Cubulating graphs of free groups with cyclic edge groups, Amer. J. Math. 132 (2010) 1153 MR2732342
32 O Kharlampovich, A Myasnikov, Elementary theory of free non-abelian groups, J. Algebra 302 (2006) 451 MR2293770
33 J C Lennox, J S Wilson, On products of subgroups in polycyclic groups, Arch. Math. (Basel) 33 (1979/80) 305 MR564284
34 G Levitt, On the automorphism group of generalized Baumslag–Solitar groups, Geom. Topol. 11 (2007) 473 MR2302496
35 R C Lyndon, P E Schupp, Combinatorial group theory, 89, Springer (1977) MR577064
36 J F Manning, E Martínez-Pedroza, Separation of relatively quasiconvex subgroups, Pacific J. Math. 244 (2010) 309 MR2587434
37 E Martínez-Pedroza, Combination of quasiconvex subgroups of relatively hyperbolic groups, Groups Geom. Dyn. 3 (2009) 317 MR2486802
38 E Martínez-Pedroza, A Sisto, Virtual amalgamation of relatively quasiconvex subgroups, Algebr. Geom. Topol. 12 (2012) 1993 MR2994828
39 K Matsuzaki, M Taniguchi, Hyperbolic manifolds and Kleinian groups, Oxford Univ. Press (1998) MR1638795
40 C McClellan, Separable at birth: products of full relatively quasi-convex subgroups, PhD thesis, University of Illinois at Chicago (2019) MR4060654
41 A Minasyan, On residualizing homomorphisms preserving quasiconvexity, Comm. Algebra 33 (2005) 2423 MR2153233
42 A Minasyan, Some properties of subsets of hyperbolic groups, Comm. Algebra 33 (2005) 909 MR2128420
43 A Minasyan, Separable subsets of GFERF negatively curved groups, J. Algebra 304 (2006) 1090 MR2264291
44 G A Niblo, Separability properties of free groups and surface groups, J. Pure Appl. Algebra 78 (1992) 77 MR1154898
45 D V Osin, Relative Dehn functions of amalgamated products and HNN-extensions, from: "Topological and asymptotic aspects of group theory" (editors R Grigorchuk, M Mihalik, M Sapir, Z Šunik), Contemp. Math. 394, Amer. Math. Soc. (2006) 209 MR2216718
46 D V Osin, Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, 843, Amer. Math. Soc. (2006) MR2182268
47 D V Osin, Peripheral fillings of relatively hyperbolic groups, Invent. Math. 167 (2007) 295 MR2270456
48 J E Pin, On a conjecture of Rhodes, Semigroup Forum 39 (1989) 1 MR987906
49 J E Pin, C Reutenauer, A conjecture on the Hall topology for the free group, Bull. London Math. Soc. 23 (1991) 356 MR1125861
50 J G Ratcliffe, Foundations of hyperbolic manifolds, 149, Springer (2006) MR2249478
51 E Reyes, On cubulated relatively hyperbolic groups, Geom. Topol. 27 (2023) 575 MR4589561
52 L Ribes, Profinite graphs and groups, 66, Springer (2017) MR3677322
53 L Ribes, P A Zalesskii, On the profinite topology on a free group, Bull. London Math. Soc. 25 (1993) 37 MR1190361
54 Z Sela, Diophantine geometry over groups, VI : The elementary theory of a free group, Geom. Funct. Anal. 16 (2006) 707 MR2238945
55 J P Serre, Trees, Springer (1980) MR607504
56 S Shepherd, D J Woodhouse, Quasi-isometric rigidity for graphs of virtually free groups with two-ended edge groups, J. Reine Angew. Math. 782 (2022) 121 MR4360010
57 H Short, Quasiconvexity and a theorem of Howson’s, from: "Group theory from a geometrical viewpoint" (editors É Ghys, A Haefliger, A Verjovsky), World Sci. Publ. (1991) 168 MR1170365
58 H Wilton, Hall’s theorem for limit groups, Geom. Funct. Anal. 18 (2008) 271 MR2399104
59 D T Wise, Subgroup separability of graphs of free groups with cyclic edge groups, Q. J. Math. 51 (2000) 107 MR1760573
60 W Yang, Combination of fully quasiconvex subgroups and its applications, preprint (2012) arXiv:1205.2994
61 S You, The product separability of the generalized free product of cyclic groups, J. Lond. Math. Soc. 56 (1997) 91 MR1462828