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

Volume 26
Issue 6, 1965–2352
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
Combination theorems for geometrically finite convergence groups

Alec Traaseth and Theodore Weisman

Algebraic & Geometric Topology 26 (2026) 2079–2122
Bibliography
1 E Alibegović, A combination theorem for relatively hyperbolic groups, Bull. London Math. Soc. 37 (2005) 459 MR2131400
2 A F Beardon, B Maskit, Limit points of Kleinian groups and finite sided fundamental polyhedra, Acta Math. 132 (1974) 1 MR333164
3 M Bestvina, M Feighn, A combination theorem for negatively curved groups, J. Differential Geom. 35 (1992) 85 MR1152226
4 J Bowden, K Mann, C0 stability of boundary actions and inequivalent Anosov flows, Ann. Sci. Éc. Norm. Supér. (4) 55 (2022) 1003 MR4468857
5 B H Bowditch, Geometrical finiteness for hyperbolic groups, J. Funct. Anal. 113 (1993) 245 MR1218098
6 B H Bowditch, Geometrical finiteness with variable negative curvature, Duke Math. J. 77 (1995) 229 MR1317633
7 B H Bowditch, Convergence groups and configuration spaces, from: "Geometric group theory down under" (editors J Cossey, I Miller Charles F., W D Neumann, M Shapiro), de Gruyter, Berlin (1999) 23 MR1714838
8 B H Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012) 1250016 MR2922380
9 F Dahmani, Combination of convergence groups, Geom. Topol. 7 (2003) 933 MR2026551
10 S Dey, M Kapovich, Klein–Maskit combination theorem for Anosov subgroups : free products, Math. Z. 305 (2023) 35 MR4647907
11 S Dey, M Kapovich, Klein–Maskit combination theorem for Anosov subgroups : amalgams, J. Reine Angew. Math. 819 (2025) 1 MR4856993
12 S Dey, M Kapovich, B Leeb, A combination theorem for Anosov subgroups, Math. Z. 293 (2019) 551 MR4002289
13 E M Freden, Negatively curved groups have the convergence property, I, Ann. Acad. Sci. Fenn. Ser. A I Math. 20 (1995) 333 MR1346817
14 F Gautero, Geodesics in trees of hyperbolic and relatively hyperbolic spaces, Proc. Edinb. Math. Soc. (2) 59 (2016) 701 MR3572767
15 F W Gehring, G J Martin, Discrete quasiconformal groups, I, Proc. London Math. Soc. (3) 55 (1987) 331 MR896224
16 R Gitik, Ping-pong on negatively curved groups, J. Algebra 217 (1999) 65 MR1700476
17 D Groves, J F Manning, Dehn filling in relatively hyperbolic groups, Israel J. Math. 168 (2008) 317 MR2448064
18 G C Hruska, Relative hyperbolicity and relative quasiconvexity for countable groups, Algebr. Geom. Topol. 10 (2010) 1807 MR2684983
19 L Li, K Ohshika, X Wang, On Klein–Maskit combination theorem in space, I, Osaka J. Math. 46 (2009) 1097 MR2604923
20 L Li, K Ohshika, X Wang, On Klein–Maskit combination theorem in space, II, Kodai Math. J. 38 (2015) 1 MR3323511
21 E Martínez-Pedroza, Combination of quasiconvex subgroups of relatively hyperbolic groups, Groups Geom. Dyn. 3 (2009) 317 MR2486802
22 E Martínez-Pedroza, A Sisto, Virtual amalgamation of relatively quasiconvex subgroups, Algebr. Geom. Topol. 12 (2012) 1993 MR2994828
23 B Maskit, Kleinian groups, 287, Springer (1988) MR959135
24 A Minasyan, L Mineh, Quasiconvexity of virtual joins and separability of products in relatively hyperbolic groups, Algebr. Geom. Topol. 25 (2025) 399 MR4885569
25 M Mj, L Reeves, A combination theorem for strong relative hyperbolicity, Geom. Topol. 12 (2008) 1777 MR2421140
26 A Pal, Height in splittings of relatively hyperbolic groups, Geom. Dedicata 213 (2021) 121 MR4278318
27 R Tomar, Boundaries of graphs of relatively hyperbolic groups with cyclic edge groups, Proc. Indian Acad. Sci. Math. Sci. 132 (2022) 47 MR4458674
28 P Tukia, Convergence groups and Gromov’s metric hyperbolic spaces, New Zealand J. Math. 23 (1994) 157 MR1313451
29 P Tukia, Conical limit points and uniform convergence groups, J. Reine Angew. Math. 501 (1998) 71 MR1637829
30 T Weisman, An extended definition of Anosov representation for relatively hyperbolic groups, J. Topol. 19 (2026) MR5054128
31 A Yaman, A topological characterisation of relatively hyperbolic groups, J. Reine Angew. Math. 566 (2004) 41 MR2039323
32 W Yang, Combination of fully quasiconvex subgroups and its applications, (2012) arXiv:1205.2994