Download this article
 Download this article For screen
For printing
Recent Issues

Volume 26
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
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