Geometry & Topology Volume 27, issue 6 (2023)

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Stable cubulations, bicombings, and barycenters

Matthew G Durham, Yair N Minsky and Alessandro Sisto

Geometry & Topology 27 (2023) 2383–2478

DOI: 10.2140/gt.2023.27.2383

Bibliography

1	J M Alonso, M R Bridson, Semihyperbolic groups, Proc. London Math. Soc. 70 (1995) 56 MR1300841
2	G Baumslag, S M Gersten, M Shapiro, H Short, Automatic groups and amalgams — a survey, from: "Algorithms and classification in combinatorial group theory" (editors G Baumslag, C F Miller III), Math. Sci. Res. Inst. Publ. 23, Springer (1992) 179 MR1230634
3	J A Behrstock, Asymptotic geometry of the mapping class group and Teichmüller space, Geom. Topol. 10 (2006) 1523 MR2255505
4	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
5	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
6	J Behrstock, M F Hagen, A Sisto, Hierarchically hyperbolic spaces, I : Curve complexes for cubical groups, Geom. Topol. 21 (2017) 1731 MR3650081
7	J Behrstock, M Hagen, A Sisto, Hierarchically hyperbolic spaces, II : Combination theorems and the distance formula, Pacific J. Math. 299 (2019) 257 MR3956144
8	J Behrstock, M F Hagen, A Sisto, Quasiflats in hierarchically hyperbolic spaces, Duke Math. J. 170 (2021) 909 MR4255047
9	J Behrstock, B Kleiner, Y Minsky, L Mosher, Geometry and rigidity of mapping class groups, Geom. Topol. 16 (2012) 781 MR2928983
10	J A Behrstock, Y N Minsky, Centroids and the rapid decay property in mapping class groups, J. Lond. Math. Soc. 84 (2011) 765 MR2855801
11	F Berlai, B Robbio, A refined combination theorem for hierarchically hyperbolic groups, Groups Geom. Dyn. 14 (2020) 1127 MR4186470
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	M Bestvina, K Bromberg, K Fujiwara, Proper actions on finite products of quasi-trees, Ann. H. Lebesgue 4 (2021) 685 MR4315766
14	M Bestvina, K Bromberg, K Fujiwara, A Sisto, Acylindrical actions on projection complexes, Enseign. Math. 65 (2019) 1 MR4057354
15	B H Bowditch, Coarse median spaces and groups, Pacific J. Math. 261 (2013) 53 MR3037559
16	B Bowditch, Convex hulls in coarse median spaces, preprint (2018)
17	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
18	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
19	P E Caprace, M Sageev, Rank rigidity for CAT(0) cube complexes, Geom. Funct. Anal. 21 (2011) 851 MR2827012
20	J Chalopin, V Chepoi, A Genevois, H Hirai, D Osajda, Helly groups, preprint (2020) arXiv:2002.06895
21	I Chatterji, G Niblo, From wall spaces to CAT(0) cube complexes, Internat. J. Algebra Comput. 15 (2005) 875 MR2197811
22	V Chepoi, Graphs of some CAT(0) complexes, Adv. in Appl. Math. 24 (2000) 125 MR1748966
23	M Chesser, Stable subgroups of the genus 2 handlebody group, Algebr. Geom. Topol. 22 (2022) 919 MR4464468
24	M T Clay, C J Leininger, J Mangahas, The geometry of right-angled Artin subgroups of mapping class groups, Groups Geom. Dyn. 6 (2012) 249 MR2914860
25	S Dowdall, M G Durham, C Leininger, A Sisto, Extensions of Veech groups, I: A hyperbolic action, preprint (2020) arXiv:2006.16425
26	S Dowdall, M G Durham, C J Leininger, A Sisto, Extensions of Veech groups, II: Hierarchical hyperbolicity and quasi-isometric rigidity, preprint (2021) arXiv:2111.00685
27	M G Durham, The augmented marking complex of a surface, J. Lond. Math. Soc. 94 (2016) 933 MR3614935
28	M G Durham, Elliptic actions on Teichmüller space, Groups Geom. Dyn. 13 (2019) 415 MR3950640
29	M G Durham, M F Hagen, A Sisto, Boundaries and automorphisms of hierarchically hyperbolic spaces, Geom. Topol. 21 (2017) 3659 MR3693574
30	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
31	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
32	A Eskin, H Masur, K Rafi, Large-scale rank of Teichmüller space, Duke Math. J. 166 (2017) 1517 MR3659941
33	S M Gersten, H B Short, Rational subgroups of biautomatic groups, Ann. of Math. 134 (1991) 125 MR1114609
34	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
35	T Haettel, N Hoda, H Petyt, Coarse injectivity, hierarchical hyperbolicity, and semihyperbolicity, preprint (2020) arXiv:2009.14053
36	M Hagen, Non-colorable hierarchically hyperbolic groups, Internat. J. Algebra Comput. 33 (2023) 337 MR4581212
37	M Hagen, A Martin, A Sisto, Extra-large type Artin groups are hierarchically hyperbolic, Math. Ann. (2022)
38	M F Hagen, T Susse, On hierarchical hyperbolicity of cubical groups, Israel J. Math. 236 (2020) 45 MR4093881
39	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. (1998) 181 MR1668359
40	U Hamenstädt, Geometry of the mapping class group, II : A biautomatic structure, preprint (2009) arXiv:0912.0137
41	G C Hruska, D T Wise, Finiteness properties of cubulated groups, Compos. Math. 150 (2014) 453 MR3187627
42	H A Masur, Y N Minsky, Geometry of the complex of curves, I : Hyperbolicity, Invent. Math. 138 (1999) 103 MR1714338
43	H A Masur, Y N Minsky, Geometry of the complex of curves, II : Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902 MR1791145
44	B Miesch, Injective metrics on cube complexes, preprint (2014) arXiv:1411.7234
45	L Mosher, Mapping class groups are automatic, Ann. of Math. 142 (1995) 303 MR1343324
46	G A Niblo, L D Reeves, The geometry of cube complexes and the complexity of their fundamental groups, Topology 37 (1998) 621 MR1604899
47	B Nica, Cubulating spaces with walls, Algebr. Geom. Topol. 4 (2004) 297 MR2059193
48	K Rafi, A combinatorial model for the Teichmüller metric, Geom. Funct. Anal. 17 (2007) 936 MR2346280
49	K Rafi, Hyperbolicity in Teichmüller space, Geom. Topol. 18 (2014) 3025 MR3285228
50	K Rafi, Y Verberne, Geodesics in the mapping class group, Algebr. Geom. Topol. 21 (2021) 2995 MR4344876
51	B Robbio, D Spriano, Hierarchical hyperbolicity of hyperbolic-2–decomposable groups, preprint (2020) arXiv:2007.13383
52	J Russell, Extensions of multicurve stabilizers are hierarchically hyperbolic, preprint (2021) arXiv:2107.14116
53	J Russell, D Spriano, H C Tran, Convexity in hierarchically hyperbolic spaces, Algebr. Geom. Topol. 23 (2023) 1167 MR4598806
54	M Sageev, Ends of group pairs and non-positively curved cube complexes, Proc. London Math. Soc. 71 (1995) 585 MR1347406
55	M Sageev, CAT(0) cube complexes and groups, from: "Geometric group theory" (editors M Bestvina, M Sageev, K Vogtmann), IAS/Park City Math. Ser. 21, Amer. Math. Soc. (2014) 7 MR3329724
56	D Spriano, Hyperbolic HHS, II : Graphs of hierarchically hyperbolic groups, preprint (2018) arXiv:1801.01850
57	P A Storm, The Novikov conjecture for mapping class groups as a corollary of Hamenstädt’s theorem, preprint (2005) arXiv:math/0504248
58	J Tao, Linearly bounded conjugator property for mapping class groups, Geom. Funct. Anal. 23 (2013) 415 MR3037904
59	A J Tromba, On a natural algebraic affine connection on the space of almost complex structures and the curvature of Teichmüller space with respect to its Weil–Petersson metric, Manuscripta Math. 56 (1986) 475 MR860734
60	S A Wolpert, Chern forms and the Riemann tensor for the moduli space of curves, Invent. Math. 85 (1986) 119 MR842050