Algebraic & Geometric Topology Volume 22, issue 7 (2022)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Projection complexes and quasimedian maps

Mark F Hagen and Harry Petyt

Algebraic & Geometric Topology 22 (2022) 3277–3304

DOI: 10.2140/agt.2022.22.3277

Bibliography

1	C Abbott, T Ng, D Spriano, R Gupta, H Petyt, Hierarchically hyperbolic groups and uniform exponential growth, preprint (2019) arXiv:1909.00439
2	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
3	J Behrstock, M F Hagen, A Sisto, Hierarchically hyperbolic spaces, I : Curve complexes for cubical groups, Geom. Topol. 21 (2017) 1731 MR3650081
4	J Behrstock, M Hagen, A Sisto, Hierarchically hyperbolic spaces II : Combination theorems and the distance formula, Pacific J. Math. 299 (2019) 257 MR3956144
5	J Behrstock, M F Hagen, A Sisto, Quasiflats in hierarchically hyperbolic spaces, Duke Math. J. 170 (2021) 909 MR4255047
6	F Berlai, B Robbio, A refined combination theorem for hierarchically hyperbolic groups, Groups Geom. Dyn. 14 (2020) 1127 MR4186470
7	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
8	M Bestvina, K Bromberg, K Fujiwara, Proper actions on finite products of quasi-trees, Ann. H. Lebesgue 4 (2021) 685 MR4315766
9	M Bestvina, K Bromberg, K Fujiwara, A Sisto, Acylindrical actions on projection complexes, Enseign. Math. 65 (2019) 1 MR4057354
10	M Bonk, O Schramm, Embeddings of Gromov hyperbolic spaces, Geom. Funct. Anal. 10 (2000) 266 MR1771428
11	B H Bowditch, Coarse median spaces and groups, Pacific J. Math. 261 (2013) 53 MR3037559
12	B H Bowditch, Convex hulls in coarse median spaces, preprint (2018.)
13	B H Bowditch, Notes on coarse median spaces, from: "Beyond hyperbolicity" (editors M Hagen, R Webb, H Wilton), London Math. Soc. Lecture Note Ser. 454, Cambridge Univ. Press (2019) 3 MR3966604
14	M R Bridson, Finiteness properties for subgroups of GL(n,Z), Math. Ann. 317 (2000) 629 MR1777113
15	N Brodskiy, J Dydak, M Levin, A Mitra, A Hurewicz theorem for the Assouad–Nagata dimension, J. Lond. Math. Soc. 77 (2008) 741 MR2418302
16	M Burger, S Mozes, Lattices in product of trees, Inst. Hautes Études Sci. Publ. Math. 92 (2000) 151 MR1839489
17	I Chatterji, C Druţu, F Haglund, Kazhdan and Haagerup properties from the median viewpoint, Adv. Math. 225 (2010) 882 MR2671183
18	V Chepoi, Graphs of some CAT(0) complexes, Adv. in Appl. Math. 24 (2000) 125 MR1748966
19	V Chepoi, F F Dragan, Y Vaxès, Core congestion is inherent in hyperbolic networks, from: "Proceedings of the Twenty-eighth Annual ACM–SIAM Symposium on Discrete Algorithms" (editor P N Klein), SIAM (2017) 2264 MR3627878
20	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
21	M G Durham, Y N Minsky, A Sisto, Stable cubulations, bicombings, and barycenters, preprint (2020) arXiv:2009.13647
22	D Gabai, Almost filling laminations and the connectivity of ending lamination space, Geom. Topol. 13 (2009) 1017 MR2470969
23	R Gitik, M Mitra, E Rips, M Sageev, Widths of subgroups, Trans. Amer. Math. Soc. 350 (1998) 321 MR1389776
24	T Haettel, N Hoda, H Petyt, Coarse injectivity, hierarchical hyperbolicity, and semihyperbolicity, preprint (2020) arXiv:2009.14053
25	M Hagen, Non-colourable hierarchically hyperbolic groups, preprint (2021)
26	M F Hagen, P Przytycki, Cocompactly cubulated graph manifolds, Israel J. Math. 207 (2015) 377 MR3358051
27	M F Hagen, T Susse, On hierarchical hyperbolicity of cubical groups, Israel J. Math. 236 (2020) 45 MR4093881
28	M F Hagen, D T Wise, Cubulating hyperbolic free-by-cyclic groups: the irreducible case, Duke Math. J. 165 (2016) 1753 MR3513573
29	F Haglund, Finite index subgroups of graph products, Geom. Dedicata 135 (2008) 167 MR2413337
30	F Haglund, F Paulin, Simplicité de groupes d’automorphismes d’espaces à courbure négative, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1, Geom. Topol. Publ. (1998) 181 MR1668359
31	F Haglund, D T Wise, A combination theorem for special cube complexes, Ann. of Math. 176 (2012) 1427 MR2979855
32	G C Hruska, D T Wise, Packing subgroups in relatively hyperbolic groups, Geom. Topol. 13 (2009) 1945 MR2497315
33	G C Hruska, D T Wise, Finiteness properties of cubulated groups, Compos. Math. 150 (2014) 453 MR3187627
34	D Hume, Embedding mapping class groups into a finite product of trees, Groups Geom. Dyn. 11 (2017) 613 MR3668054
35	S H Kim, T Koberda, The geometry of the curve graph of a right-angled Artin group, Internat. J. Algebra Comput. 24 (2014) 121 MR3192368
36	C J Leininger, D B McReynolds, Separable subgroups of mapping class groups, Topology Appl. 154 (2007) 1 MR2271769
37	H A Masur, Y N Minsky, Geometry of the complex of curves, II : Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902 MR1791145
38	G A Niblo, L D Reeves, Coxeter groups act on CAT(0) cube complexes, J. Group Theory 6 (2003) 399 MR1983376
39	B Nica, Cubulating spaces with walls, Algebr. Geom. Topol. 4 (2004) 297 MR2059193
40	H Petyt, D Spriano, Unbounded domains in hierarchically hyperbolic groups, preprint (2020) arXiv:2007.12535
41	M Roller, Poc sets, median algebras and group actions, preprint (2016) arXiv:1607.07747
42	J Russell, D Spriano, H C Tran, Convexity in hierarchically hyperbolic spaces, preprint (2018) arXiv:1809.09303
43	M Sageev, Codimension-1 subgroups and splittings of groups, J. Algebra 189 (1997) 377 MR1438181
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	D T Wise, Complete square complexes, Comment. Math. Helv. 82 (2007) 683 MR2341837
46	N Wright, Finite asymptotic dimension for CAT(0) cube complexes, Geom. Topol. 16 (2012) 527 MR2916293