Algebraic & Geometric Topology Volume 25, issue 4 (2025)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Generalised Baumslag–Solitar groups and hierarchically hyperbolic groups

Jack O Button

Algebraic & Geometric Topology 25 (2025) 2253–2279

DOI: 10.2140/agt.2025.25.2253

Bibliography

1	C Abbott, S H Balasubramanya, D Osin, Hyperbolic structures on groups, Algebr. Geom. Topol. 19 (2019) 1747 MR3995018
2	C R Abbott, T Ng, D Spriano, R Gupta, H Petyt, Hierarchically hyperbolic groups and uniform exponential growth, Math. Z. 306 (2024) 18 MR4680503
3	B Beeker, Abelian JSJ decomposition of graphs of free abelian groups, J. Group Theory 17 (2014) 337 MR3176664
4	J Behrstock, M F Hagen, A Sisto, Hierarchically hyperbolic spaces, I : Curve complexes for cubical groups, Geom. Topol. 21 (2017) 1731 MR3650081
5	J Behrstock, M Hagen, A Sisto, Hierarchically hyperbolic spaces, II : Combination theorems and the distance formula, Pacific J. Math. 299 (2019) 257 MR3956144
6	M Bestvina, K Bromberg, K Fujiwara, Proper actions on finite products of quasi-trees, Ann. H. Lebesgue 4 (2021) 685 MR4315766
7	O Bogopolski, A Martino, E Ventura, Orbit decidability and the conjugacy problem for some extensions of groups, Trans. Amer. Math. Soc. 362 (2010) 2003 MR2574885
8	B H Bowditch, Tight geodesics in the curve complex, Invent. Math. 171 (2008) 281 MR2367021
9	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
10	P E Caprace, Y Cornulier, N Monod, R Tessera, Amenable hyperbolic groups, J. Eur. Math. Soc. 17 (2015) 2903 MR3420526
11	M Casals-Ruiz, I Kazachkov, A Zakharov, Commensurability of Baumslag–Solitar groups, Indiana Univ. Math. J. 70 (2021) 2527 MR4359918
12	C H Cashen, G Levitt, Mapping tori of free group automorphisms, and the Bieri–Neumann–Strebel invariant of graphs of groups, J. Group Theory 19 (2016) 191 MR3466593
13	Y de Cornulier, R Tessera, Metabelian groups with quadratic Dehn function and Baumslag–Solitar groups, Confluentes Math. 2 (2010) 431 MR2764812
14	Y Cornulier, A Valette, On equivariant embeddings of generalized Baumslag–Solitar groups, Geom. Dedicata 175 (2015) 385 MR3323648
15	R B Coulon, Partial periodic quotients of groups acting on a hyperbolic space, Ann. Inst. Fourier (Grenoble) 66 (2016) 1773 MR3533270
16	A Dranishnikov, T Januszkiewicz, Every Coxeter group acts amenably on a compact space, Topology Proc. 24 (1999) 135 MR1802681
17	M G Durham, M F Hagen, A Sisto, Boundaries and automorphisms of hierarchically hyperbolic spaces, Geom. Topol. 21 (2017) 3659 MR3693574
18	M G Durham, M F Hagen, A Sisto, Correction to the article Boundaries and automorphisms of hierarchically hyperbolic spaces, Geom. Topol. 24 (2020) 1051 MR4153656
19	T Foertsch, A Lytchak, The de Rham decomposition theorem for metric spaces, Geom. Funct. Anal. 18 (2008) 120 MR2399098
20	M Forester, Deformation and rigidity of simplicial group actions on trees, Geom. Topol. 6 (2002) 219 MR1914569
21	M F Hagen, Cocompactly cubulated crystallographic groups, J. Lond. Math. Soc. 90 (2014) 140 MR3245140
22	M Hagen, J Russell, A Sisto, D Spriano, Equivariant hierarchically hyperbolic structures for 3-manifold groups via quasimorphisms, Ann. Inst. Fourier (Grenoble) (2024)
23	P de la Harpe, Topics in geometric group theory, Univ. Chicago Press (2000) MR1786869
24	J Huang, T Prytuła, Commensurators of abelian subgroups in CAT(0) groups, Math. Z. 296 (2020) 79 MR4140732
25	S Hughes, M Valiunas, Commensurating HNN-extensions : hierarchical hyperbolicity and biautomaticity, Comment. Math. Helv. 99 (2024) 397 MR4730350
26	M Koubi, Croissance uniforme dans les groupes hyperboliques, Ann. Inst. Fourier (Grenoble) 48 (1998) 1441 MR1662255
27	P H Kropholler, Baumslag–Solitar groups and some other groups of cohomological dimension two, Comment. Math. Helv. 65 (1990) 547 MR1078097
28	I J Leary, A Minasyan, Commensurating HNN extensions : nonpositive curvature and biautomaticity, Geom. Topol. 25 (2021) 1819 MR4286364
29	G Levitt, On the automorphism group of generalized Baumslag–Solitar groups, Geom. Topol. 11 (2007) 473 MR2302496
30	W Malone, Isometries of products of path-connected locally uniquely geodesic metric spaces with the sup metric are reducible, preprint (2009) arXiv:0912.3471
31	J F Manning, Quasi-actions on trees and property (QFA), J. Lond. Math. Soc. 73 (2006) 84 MR2197372
32	A Minasyan, D Osin, Acylindrical hyperbolicity of groups acting on trees, Math. Ann. 362 (2015) 1055 MR3368093
33	D Osin, Acylindrically hyperbolic groups, Trans. Amer. Math. Soc. 368 (2016) 851 MR3430352
34	H Petyt, D Spriano, Unbounded domains in hierarchically hyperbolic groups, Groups Geom. Dyn. 17 (2023) 479 MR4584673