Geometry & Topology Volume 29, issue 6 (2025)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Extensions of multicurve stabilizers are hierarchically hyperbolic

Jacob Russell

Geometry & Topology 29 (2025) 3187–3240

DOI: 10.2140/gt.2025.29.3187

Bibliography

1	C Abbott, S H Balasubramanya, D Osin, Hyperbolic structures on groups, Algebr. Geom. Topol. 19 (2019) 1747 MR3995018
2	C Abbott, J Behrstock, M G Durham, Largest acylindrical actions and stability in hierarchically hyperbolic groups, Trans. Amer. Math. Soc. Ser. B 8 (2021) 66 MR4215647
3	T Aougab, Uniform hyperbolicity of the graphs of curves, Geom. Topol. 17 (2013) 2855 MR3190300
4	J A Behrstock, Asymptotic geometry of the mapping class group and Teichmüller space, Geom. Topol. 10 (2006) 1523 MR2255505
5	J A Behrstock, Y N Minsky, Dimension and rank for mapping class groups, Ann. of Math. 167 (2008) 1055 MR2415393
6	J Behrstock, B Kleiner, Y Minsky, L Mosher, Geometry and rigidity of mapping class groups, Geom. Topol. 16 (2012) 781 MR2928983
7	J Behrstock, M F Hagen, A Sisto, Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups, Proc. Lond. Math. Soc. 114 (2017) 890 MR3653249
8	J Behrstock, M F Hagen, A Sisto, Hierarchically hyperbolic spaces, I : Curve complexes for cubical groups, Geom. Topol. 21 (2017) 1731 MR3650081
9	J Behrstock, M Hagen, A Sisto, Hierarchically hyperbolic spaces, II : Combination theorems and the distance formula, Pacific J. Math. 299 (2019) 257 MR3956144
10	J Behrstock, M F Hagen, A Sisto, Quasiflats in hierarchically hyperbolic spaces, Duke Math. J. 170 (2021) 909 MR4255047
11	J Behrstock, M Hagen, A Martin, A Sisto, A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups, J. Topol. 17 (2024) MR4822919
12	F Berlai, B Robbio, A refined combination theorem for hierarchically hyperbolic groups, Groups Geom. Dyn. 14 (2020) 1127 MR4186470
13	D Berlyne, J Russell, Hierarchical hyperbolicity of graph products, Groups Geom. Dyn. 16 (2022) 523 MR4502615
14	M Bestvina, K Bromberg, A E Kent, C J Leininger, Undistorted purely pseudo-Anosov groups, J. Reine Angew. Math. 760 (2020) 213 MR4069890
15	B H Bowditch, Intersection numbers and the hyperbolicity of the curve complex, J. Reine Angew. Math. 598 (2006) 105 MR2270568
16	B H Bowditch, Uniform hyperbolicity of the curve graphs, Pacific J. Math. 269 (2014) 269 MR3238474
17	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
18	J F Brock, The Weil–Petersson metric and volumes of 3-dimensional hyperbolic convex cores, J. Amer. Math. Soc. 16 (2003) 495 MR1969203
19	R Charney, M Cordes, A Sisto, Complete topological descriptions of certain Morse boundaries, Groups Geom. Dyn. 17 (2023) 157 MR4563334
20	M Chesser, Stable subgroups of the genus 2 handlebody group, Algebr. Geom. Topol. 22 (2022) 919 MR4464468
21	M Clay, K Rafi, S Schleimer, Uniform hyperbolicity of the curve graph via surgery sequences, Algebr. Geom. Topol. 14 (2014) 3325 MR3302964
22	M Cordes, A survey on Morse boundaries and stability, from: "Beyond hyperbolicity" (editors M Hagen, R Webb, H Wilton), London Math. Soc. Lecture Note Ser. 454, Cambridge Univ. Press (2019) 83 MR3966607
23	M Cordes, M G Durham, Boundary convex cocompactness and stability of subgroups of finitely generated groups, Int. Math. Res. Not. 2019 (2019) 1699 MR3932592
24	M Cordes, D Hume, Stability and the Morse boundary, J. Lond. Math. Soc. 95 (2017) 963 MR3664526
25	S Dowdall, M G Durham, C J Leininger, A Sisto, Extensions of Veech groups, II : Hierarchical hyperbolicity and quasi-isometric rigidity, Comment. Math. Helv. 99 (2024) 149 MR4709309
26	M G Durham, The augmented marking complex of a surface, J. Lond. Math. Soc. 94 (2016) 933 MR3614935
27	M G Durham, S J Taylor, Convex cocompactness and stability in mapping class groups, Algebr. Geom. Topol. 15 (2015) 2839 MR3426695
28	A Eskin, H Masur, K Rafi, Large-scale rank of Teichmüller space, Duke Math. J. 166 (2017) 1517 MR3659941
29	T Haettel, N Hoda, H Petyt, Coarse injectivity, hierarchical hyperbolicity and semihyperbolicity, Geom. Topol. 27 (2023) 1587 MR4602421
30	M F Hagen, T Susse, On hierarchical hyperbolicity of cubical groups, Israel J. Math. 236 (2020) 45 MR4093881
31	M Hagen, A Martin, A Sisto, Extra-large type Artin groups are hierarchically hyperbolic, Math. Ann. 388 (2024) 867 MR4693949
32	U Hamenstaedt, Word hyperbolic extensions of surface groups, preprint (2005) arXiv:math/0505244
33	S Hensel, P Przytycki, R C H Webb, 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs, J. Eur. Math. Soc. 17 (2015) 755 MR3336835
34	A E Kent, C J Leininger, Subgroups of mapping class groups from the geometrical viewpoint, from: "In the tradition of Ahlfors–Bers, IV" (editors D Canary, J Gilman, J Heinonen, H Masur), Contemp. Math. 432, Amer. Math. Soc. (2007) 119 MR2342811
35	A E Kent, C J Leininger, S Schleimer, Trees and mapping class groups, J. Reine Angew. Math. 637 (2009) 1 MR2599078
36	J F Manning, Geometry of pseudocharacters, Geom. Topol. 9 (2005) 1147 MR2174263
37	H A Masur, Y N Minsky, Geometry of the complex of curves, I : Hyperbolicity, Invent. Math. 138 (1999) 103 MR1714338
38	H A Masur, Y N Minsky, Geometry of the complex of curves, II : Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902 MR1791145
39	M Mj, P Sardar, A combination theorem for metric bundles, Geom. Funct. Anal. 22 (2012) 1636 MR3000500
40	J P Otal, Le théorème d’hyperbolisation pour les variétés fibrées de dimension 3, 235, Soc. Math. France (1996) MR1402300
41	K Rafi, A combinatorial model for the Teichmüller metric, Geom. Funct. Anal. 17 (2007) 936 MR2346280
42	J Russell, D Spriano, H C Tran, The local-to-global property for Morse quasi-geodesics, Math. Z. 300 (2022) 1557 MR4363788
43	J Russell, D Spriano, H C Tran, Convexity in hierarchically hyperbolic spaces, Algebr. Geom. Topol. 23 (2023) 1167 MR4598806
44	A Sisto, What is a hierarchically hyperbolic space?, from: "Beyond hyperbolicity" (editors M Hagen, R Webb, H Wilton), London Math. Soc. Lecture Note Ser. 454, Cambridge Univ. Press (2019) 117 MR3966608
45	K M Vokes, Hierarchical hyperbolicity of graphs of multicurves, Algebr. Geom. Topol. 22 (2022) 113 MR4413817