Volume 22, issue 3 (2022)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 9, 4731–5219
Issue 8, 4139–4730
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Sublinearly Morse geodesics in CAT(0) spaces: lower divergence and hyperplane characterization

Devin Murray, Yulan Qing and Abdul Zalloum

Algebraic & Geometric Topology 22 (2022) 1337–1374
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 Y Algom-Kfir, Strongly contracting geodesics in outer space, Geom. Topol. 15 (2011) 2181 MR2862155
3 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
4 W Ballmann, S Buyalo, Periodic rank one geodesics in Hadamard spaces, from: "Geometric and probabilistic structures in dynamics" (editors K Burns, D Dolgopyat, Y Pesin), Contemp. Math. 469, Amer. Math. Soc. (2008) 19 MR2478464
5 J Behrstock, R Charney, Divergence and quasimorphisms of right-angled Artin groups, Math. Ann. 352 (2012) 339 MR2874959
6 J Behrstock, M F Hagen, A Sisto, Hierarchically hyperbolic spaces, I : Curve complexes for cubical groups, Geom. Topol. 21 (2017) 1731 MR3650081
7 M Bestvina, K Fujiwara, A characterization of higher rank symmetric spaces via bounded cohomology, Geom. Funct. Anal. 19 (2009) 11 MR2507218
8 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
9 P E Caprace, M Sageev, Rank rigidity for CAT(0) cube complexes, Geom. Funct. Anal. 21 (2011) 851 MR2827012
10 R Charney, H Sultan, Contracting boundaries of CAT(0) spaces, J. Topol. 8 (2015) 93 MR3339446
11 M Cordes, Morse boundaries of proper geodesic metric spaces, Groups Geom. Dyn. 11 (2017) 1281 MR3737283
12 M Cordes, M Dussaule, I Gekhtman, An embedding of the Morse boundary in the Martin boundary, preprint (2020) arXiv:2004.14624
13 C B Croke, B Kleiner, Spaces with nonpositive curvature and their ideal boundaries, Topology 39 (2000) 549 MR1746908
14 M Duchin, K Rafi, Divergence of geodesics in Teichmüller space and the mapping class group, Geom. Funct. Anal. 19 (2009) 722 MR2563768
15 I Gekhtman, Y Qing, K Rafi, Genericity of sublinearly Morse geodesics, in preparation
16 A Genevois, Hyperbolicities in CAT(0) cube complexes, Enseign. Math. 65 (2019) 33 MR4057355
17 A Genevois, Contracting isometries of CAT(0) cube complexes and acylindrical hyperbolicity of diagram groups, Algebr. Geom. Topol. 20 (2020) 49 MR4071367
18 S M Gersten, Quadratic divergence of geodesics in CAT(0) spaces, Geom. Funct. Anal. 4 (1994) 37 MR1254309
19 M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
20 M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, 2" (editors G A Niblo, M A Roller, J W S Cassels), London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1 MR1253544
21 M F Hagen, Weak hyperbolicity of cube complexes and quasi-arboreal groups, J. Topol. 7 (2014) 385 MR3217625
22 M Hagen, Large facing tuples and a strengthened sector lemma, Tunis. J. Math. 4 (2022) 55 MR4401788
23 U Hamenstädt, Rank-one isometries of proper CAT(0)–spaces, from: "Discrete groups and geometric structures" (editors K Dekimpe, P Igodt, A Valette), Contemp. Math. 501, Amer. Math. Soc. (2009) 43 MR2581914
24 M Incerti-Medici, Comparing topologies on the Morse boundary and quasi-isometry invariance, Geom. Dedicata 212 (2021) 153 MR4251668
25 I Kapovich, N Benakli, Boundaries of hyperbolic groups, from: "Combinatorial and geometric group theory" (editors S Cleary, R Gilman, A G Myasnikov, V Shpilrain), Contemp. Math. 296, Amer. Math. Soc. (2002) 39 MR1921706
26 I Levcovitz, Divergence of CAT(0) cube complexes and Coxeter groups, Algebr. Geom. Topol. 18 (2018) 1633 MR3784015
27 D Murray, Topology and dynamics of the contracting boundary of cocompact CAT(0) spaces, Pacific J. Math. 299 (2019) 89 MR3947271
28 Y Qing, K Rafi, Sublinearly Morse boundary, I : CAT(0) spaces, Adv. Math. 404 (2022) MR4423805
29 Y Qing, K Rafi, G Tiozzo, Sublinearly Morse boundary, II : Proper geodesic spaces, preprint (2020) arXiv:2011.03481
30 Y Qing, A Zalloum, Rank one isometries in sublinearly Morse boundaries of CAT(0) groups, preprint (2019) arXiv:1911.03296