Geometry & Topology Volume 27, issue 4 (2023)

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Coarse injectivity, hierarchical hyperbolicity and semihyperbolicity

Thomas Haettel, Nima Hoda and Harry Petyt

Geometry & Topology 27 (2023) 1587–1633

DOI: 10.2140/gt.2023.27.1587

Bibliography

1	C Abbott, J Behrstock, Conjugator lengths in hierarchically hyperbolic groups, preprint (2018) arXiv:1808.09604
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	C Abbott, T Ng, D Spriano, R Gupta, H Petyt, Hierarchically hyperbolic groups and uniform exponential growth, preprint (2019) arXiv:1909.00439
4	J M Alonso, M R Bridson, Semihyperbolic groups, Proc. London Math. Soc. 70 (1995) 56 MR1300841
5	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
6	N Aronszajn, P Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956) 405 MR84762
7	H J Bandelt, M van de Vel, Superextensions and the depth of median graphs, J. Combin. Theory Ser. A 57 (1991) 187 MR1111556
8	J Behrstock, C Druţu, Divergence, thick groups, and short conjugators, Illinois J. Math. 58 (2014) 939 MR3421592
9	J Behrstock, M Hagen, A Martin, A Sisto, A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups, preprint (2020) arXiv:2005.00567
10	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
11	J Behrstock, M F Hagen, A Sisto, Hierarchically hyperbolic spaces, I : Curve complexes for cubical groups, Geom. Topol. 21 (2017) 1731 MR3650081
12	J Behrstock, M F Hagen, A Sisto, Quasiflats in hierarchically hyperbolic spaces, preprint (2017) arXiv:1704.04271
13	J Behrstock, M Hagen, A Sisto, Hierarchically hyperbolic spaces, II : Combination theorems and the distance formula, Pacific J. Math. 299 (2019) 257 MR3956144
14	J A Behrstock, Y N Minsky, Centroids and the rapid decay property in mapping class groups, J. Lond. Math. Soc. 84 (2011) 765 MR2855801
15	F Berlai, B Robbio, A refined combination theorem for hierarchically hyperbolic groups, Groups Geom. Dyn. 14 (2020) 1127 MR4186470
16	D Berlyne, J Russell, Hierarchical hyperbolicity of graph products, Groups Geom. Dyn. 16 (2022) 523 MR4502615
17	B H Bowditch, Coarse median spaces and groups, Pacific J. Math. 261 (2013) 53 MR3037559
18	B Bowditch, Convex hulls in coarse median spaces, preprint (2019)
19	B Bowditch, Quasiflats in coarse median spaces, preprint (2019)
20	B H Bowditch, Median and injective metric spaces, Math. Proc. Cambridge Philos. Soc. 168 (2020) 43 MR4043820
21	M R Bridson, Finiteness properties for subgroups of GL(n, ℤ), Math. Ann. 317 (2000) 629 MR1777113
22	M R Bridson, Semisimple actions of mapping class groups on CAT(0) spaces, from: "Geometry of Riemann surfaces" (editors F P Gardiner, G González-Diez, C Kourouniotis), London Math. Soc. Lecture Note Ser. 368, Cambridge Univ. Press (2010) 1 MR2665003
23	M R Bridson, Semihyperbolicity, from: "Beyond hyperbolicity" (editors M Hagen, R Webb, H Wilton), London Math. Soc. Lecture Note Ser. 454, Cambridge Univ. Press (2019) 25 MR3966605
24	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
25	P E Caprace, M Sageev, Rank rigidity for CAT(0) cube complexes, Geom. Funct. Anal. 21 (2011) 851 MR2827012
26	J Chalopin, V Chepoi, A Genevois, H Hirai, D Osajda, Helly groups, preprint (2020) arXiv:2002.06895
27	V Chepoi, Separation of two convex sets in convexity structures, J. Geom. 50 (1994) 30 MR1280625
28	V Chepoi, Graphs of some CAT(0) complexes, Adv. in Appl. Math. 24 (2000) 125 MR1748966
29	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
30	V Chepoi, B Estellon, Packing and covering δ–hyperbolic spaces by balls, from: "Approximation, randomization, and combinatorial optimization: algorithms and techniques" (editors M Charikar, K Jansen, O Reingold, J D P Rolim), Lecture Notes in Computer Science 4627, Springer (2007) 59
31	M Chesser, Stable subgroups of the genus 2 handlebody group, Algebr. Geom. Topol. 22 (2022) 919 MR4464468
32	M Chrobak, L L Larmore, Generosity helps or an 11–competitive algorithm for three servers, J. Algorithms 16 (1994) 234 MR1258238
33	Y Cornulier, P de la Harpe, Metric geometry of locally compact groups, 25, Eur. Math. Soc. (2016) MR3561300
34	D Descombes, U Lang, Convex geodesic bicombings and hyperbolicity, Geom. Dedicata 177 (2015) 367 MR3370039
35	S Dowdall, M G Durham, C J Leininger, A Sisto, Extensions of Veech groups, I: A hyperbolic action, preprint (2020) arXiv:2006.16425
36	A W M Dress, Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: a note on combinatorial properties of metric spaces, Adv. in Math. 53 (1984) 321 MR753872
37	M G Durham, M F Hagen, A Sisto, Boundaries and automorphisms of hierarchically hyperbolic spaces, Geom. Topol. 21 (2017) 3659 MR3693574
38	M G Durham, Y N Minsky, A Sisto, Stable cubulations, bicombings, and barycenters, preprint (2020) arXiv:2009.13647
39	M G Durham, S J Taylor, Convex cocompactness and stability in mapping class groups, Algebr. Geom. Topol. 15 (2015) 2839 MR3426695
40	A Engel, C Wulff, Coronas for properly combable spaces, preprint (2017) arXiv:1711.06836
41	D B A Epstein, J W Cannon, D F Holt, S V F Levy, M S Paterson, W P Thurston, Word processing in groups, Jones and Bartlett (1992) MR1161694
42	T Fukaya, S i Oguni, A coarse Cartan–Hadamard theorem with application to the coarse Baum–Connes conjecture, J. Topol. Anal. 12 (2020) 857 MR4139217
43	A Genevois, Hyperbolicities in CAT(0) cube complexes, Enseign. Math. 65 (2019) 33 MR4057355
44	A Genevois, Median sets of isometries in CAT(0) cube complexes and some applications, preprint (2019) arXiv:1902.04883
45	R Gitik, M Mitra, E Rips, M Sageev, Widths of subgroups, Trans. Amer. Math. Soc. 350 (1998) 321 MR1389776
46	T Haettel, Hyperbolic rigidity of higher rank lattices, Ann. Sci. Éc. Norm. Supér. 53 (2020) 439 MR4094562
47	M F Hagen, H Petyt, Projection complexes and quasimedian maps, Algebr. Geom. Topol. 22 (2022) 3277 MR4545918
48	M F Hagen, T Susse, On hierarchical hyperbolicity of cubical groups, Israel J. Math. 236 (2020) 45 MR4093881
49	U Hamenstaedt, Geometry of the mapping class group, II: A biautomatic structure, preprint (2009) arXiv:0912.0137
50	N Hoda, Crystallographic Helly groups, preprint (2020) arXiv:2010.07407
51	N Hoda, Strongly shortcut spaces, preprint (2020) arXiv:2010.07400
52	N Hoda, Shortcut graphs and groups, Trans. Amer. Math. Soc. 375 (2022) 2417 MR4391723
53	G C Hruska, D T Wise, Packing subgroups in relatively hyperbolic groups, Geom. Topol. 13 (2009) 1945 MR2497315
54	G C Hruska, D T Wise, Finiteness properties of cubulated groups, Compos. Math. 150 (2014) 453 MR3187627
55	J Huang, D Osajda, Helly meets Garside and Artin, Invent. Math. 225 (2021) 395 MR4285138
56	S Hughes, M Valiunas, Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity, preprint (2022) arXiv:2203.11996
57	J R Isbell, Six theorems about injective metric spaces, Comment. Math. Helv. 39 (1964) 65 MR182949
58	M Kapovich, B Leeb, Actions of discrete groups on nonpositively curved spaces, Math. Ann. 306 (1996) 341 MR1411351
59	S P Kerckhoff, The Nielsen realization problem, Ann. of Math. 117 (1983) 235 MR690845
60	U Lang, Injective hulls of certain discrete metric spaces and groups, J. Topol. Anal. 5 (2013) 297 MR3096307
61	H A Masur, Y N Minsky, Geometry of the complex of curves, II : Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902 MR1791145
62	L Mosher, Mapping class groups are automatic, Ann. of Math. 142 (1995) 303 MR1343324
63	G A Niblo, L D Reeves, The geometry of cube complexes and the complexity of their fundamental groups, Topology 37 (1998) 621 MR1604899
64	G A Niblo, L D Reeves, Coxeter groups act on CAT(0) cube complexes, J. Group Theory 6 (2003) 399 MR1983376
65	G A Niblo, N Wright, J Zhang, A four point characterisation for coarse median spaces, Groups Geom. Dyn. 13 (2019) 939 MR4002223
66	H Petyt, D Spriano, Unbounded domains in hierarchically hyperbolic groups, Groups Geom. Dyn. 17 (2023) 479 MR4584673
67	P Plummer, Some graph manifold groups are not hierarchically hyperbolic groups, preprint (2020)
68	B Robbio, D Spriano, Hierarchical hyperbolicity of hyperbolic-2–decomposable groups, preprint (2020) arXiv:2007.13383
69	M Roller, Poc sets, median algebras and group actions, Habilitationsschrift, Universität Regensburg (1998) arXiv:1607.07747
70	H Rubinstein, M Sageev, Intersection patterns of essential surfaces in 3–manifolds, Topology 38 (1999) 1281 MR1690158
71	J Russell, D Spriano, H C Tran, Convexity in hierarchically hyperbolic spaces, preprint (2018) arXiv:1809.09303
72	M Sageev, Codimension-1 subgroups and splittings of groups, J. Algebra 189 (1997) 377 MR1438181
73	A Sisto, Quasi-convexity of hyperbolically embedded subgroups, Math. Z. 283 (2016) 649 MR3519976
74	J Tao, Linearly bounded conjugator property for mapping class groups, Geom. Funct. Anal. 23 (2013) 415 MR3037904
75	H C Tran, On strongly quasiconvex subgroups, Geom. Topol. 23 (2019) 1173 MR3956891
76	K M Vokes, Hierarchical hyperbolicity of graphs of multicurves, Algebr. Geom. Topol. 22 (2022) 113 MR4413817