Algebraic & Geometric Topology Volume 23, issue 3 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

Convexity in hierarchically hyperbolic spaces

Jacob Russell, Davide Spriano and Hung Cong Tran

Algebraic & Geometric Topology 23 (2023) 1167–1248

DOI: 10.2140/agt.2023.23.1167

Bibliography

1	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
2	I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553
3	Y Antolín, M Mj, A Sisto, S J Taylor, Intersection properties of stable subgroups and bounded cohomology, Indiana Univ. Math. J. 68 (2019) 179 MR3922043
4	T Aougab, M G Durham, S J Taylor, Pulling back stability with applications to Out(F_n) and relatively hyperbolic groups, J. Lond. Math. Soc. 96 (2017) 565 MR3742433
5	G N Arzhantseva, On quasiconvex subgroups of word hyperbolic groups, Geom. Dedicata 87 (2001) 191 MR1866849
6	G N Arzhantseva, C H Cashen, D Gruber, D Hume, Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction, Doc. Math. 22 (2017) 1193 MR3690269
7	J Behrstock, A counterexample to questions about boundaries, stability, and commensurability, from: "Beyond hyperbolicity" (editors M Hagen, R Webb, H Wilton), London Math. Soc. Lecture Note Ser. 454, Cambridge Univ. Press (2019) 151 MR3966609
8	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
9	J Behrstock, M F Hagen, A Sisto, Hierarchically hyperbolic spaces, I : Curve complexes for cubical groups, Geom. Topol. 21 (2017) 1731 MR3650081
10	J Behrstock, M Hagen, A Sisto, Hierarchically hyperbolic spaces II : Combination theorems and the distance formula, Pacific J. Math. 299 (2019) 257 MR3956144
11	J Behrstock, M F Hagen, A Sisto, Quasiflats in hierarchically hyperbolic spaces, Duke Math. J. 170 (2021) 909 MR4255047
12	M Bestvina, K Bromberg, K Fujiwara, Constructing group actions on quasi-trees and applications to mapping class groups, Publ. Math. Inst. Hautes Études Sci. 122 (2015) 1 MR3415065
13	B H Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012) 1250016 MR2922380
14	B H Bowditch, Coarse median spaces and groups, Pacific J. Math. 261 (2013) 53 MR3037559
15	B H Bowditch, Uniform hyperbolicity of the curve graphs, Pacific J. Math. 269 (2014) 269 MR3238474
16	B , H., Convex hulls in coarse median spaces, preprint (2018)
17	J F Brock, The Weil–Petersson metric and volumes of 3–dimensional hyperbolic convex cores, J. Amer. Math. Soc. 16 (2003) 495 MR1969203
18	C H Cashen, Morse subsets of CAT(0) spaces are strongly contracting, Geom. Dedicata 204 (2020) 311 MR4056705
19	R Charney, H Sultan, Contracting boundaries of CAT(0) spaces, J. Topol. 8 (2015) 93 MR3339446
20	F Dahmani, V Guirardel, D Osin, Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces, 1156, Amer. Math. Soc. (2017) MR3589159
21	C Druţu, M Kapovich, Geometric group theory, 63, Amer. Math. Soc. (2018) MR3753580
22	C Druţu, S Mozes, M Sapir, Divergence in lattices in semisimple Lie groups and graphs of groups, Trans. Amer. Math. Soc. 362 (2010) 2451 MR2584607
23	M G Durham, The augmented marking complex of a surface, J. Lond. Math. Soc. 94 (2016) 933 MR3614935
24	M G Durham, M F Hagen, A Sisto, Boundaries and automorphisms of hierarchically hyperbolic spaces, Geom. Topol. 21 (2017) 3659 MR3693574
25	M G Durham, S J Taylor, Convex cocompactness and stability in mapping class groups, Algebr. Geom. Topol. 15 (2015) 2839 MR3426695
26	A Eskin, H Masur, K Rafi, Large-scale rank of Teichmüller space, Duke Math. J. 166 (2017) 1517 MR3659941
27	B Farb, Some problems on mapping class groups and moduli space, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 11 MR2264130
28	A Genevois, Hyperbolicities in CAT(0) cube complexes, Enseign. Math. 65 (2019) 33 MR4057355
29	A Genevois, Quasi-isometrically rigid subgroups in right-angled Coxeter groups, Algebr. Geom. Topol. 22 (2022) 657 MR4464462
30	R Gitik, Ping-pong on negatively curved groups, J. Algebra 217 (1999) 65 MR1700476
31	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
32	M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, II" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1 MR1253544
33	D Groves, J F Manning, Hyperbolic groups acting improperly, preprint (2018) arXiv:1808.02325
34	T Haettel, Hyperbolic rigidity of higher rank lattices, Ann. Sci. Éc. Norm. Supér. 53 (2020) 439 MR4094562
35	M F Hagen, H Petyt, Projection complexes and quasimedian maps, Algebr. Geom. Topol. 22 (2022) 3277 MR4545918
36	G C Hruska, Relative hyperbolicity and relative quasiconvexity for countable groups, Algebr. Geom. Topol. 10 (2010) 1807 MR2684983
37	A Karrer, Right-angled Coxeter groups with totally disconnected Morse boundaries, preprint (2021) arXiv:2105.04029
38	H Kim, Stable subgroups and Morse subgroups in mapping class groups, Internat. J. Algebra Comput. 29 (2019) 893 MR3978121
39	T Koberda, J Mangahas, S J Taylor, The geometry of purely loxodromic subgroups of right-angled Artin groups, Trans. Amer. Math. Soc. 369 (2017) 8179 MR3695858
40	H A Masur, Y N Minsky, Geometry of the complex of curves, I : Hyperbolicity, Invent. Math. 138 (1999) 103 MR1714338
41	H A Masur, Y N Minsky, Geometry of the complex of curves, II : Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902 MR1791145
42	H Masur, S Schleimer, The geometry of the disk complex, J. Amer. Math. Soc. 26 (2013) 1 MR2983005
43	H T Nguyen, H C Tran, On the coarse geometry of certain right-angled Coxeter groups, Algebr. Geom. Topol. 19 (2019) 3075 MR4023336
44	A Y Ol’shanskii, D V Osin, M V Sapir, Lacunary hyperbolic groups, Geom. Topol. 13 (2009) 2051 MR2507115
45	D Osin, Acylindrically hyperbolic groups, Trans. Amer. Math. Soc. 368 (2016) 851 MR3430352
46	N Petrosyan, Decomposing groups by codimension-1 subgroups, Proc. Amer. Math. Soc. 150 (2022) 4587 MR4489298
47	K Rafi, A combinatorial model for the Teichmüller metric, Geom. Funct. Anal. 17 (2007) 936 MR2346280
48	J Russell, From hierarchical to relative hyperbolicity, Int. Math. Res. Not. 2022 (2022) 575 MR4366027
49	A Sisto, On metric relative hyperbolicity, preprint (2012) arXiv:1210.8081
50	A Sisto, Quasi-convexity of hyperbolically embedded subgroups, Math. Z. 283 (2016) 649 MR3519976
51	D Spriano, Hyperbolic HHS, II : Graphs of hierarchically hyperbolic groups, preprint (2018) arXiv:1801.01850
52	H Sultan, Hyperbolic quasi-geodesics in CAT(0) spaces, Geom. Dedicata 169 (2014) 209 MR3175245
53	H C Tran, Relative divergence of finitely generated groups, Algebr. Geom. Topol. 15 (2015) 1717 MR3361149
54	H C Tran, On strongly quasiconvex subgroups, Geom. Topol. 23 (2019) 1173 MR3956891
55	D T Wise, From riches to raags : 3–manifolds, right-angled Artin groups, and cubical geometry, 117, Amer. Math. Soc. (2012) MR2986461